What's the minimum (physics first) to get an oscillator? - Page 1
Forum section: electronics / general

author: RoGeorge
author_rank: Super Contributor
timestamp: May 23, 2023, 01:00:33 pm
content: As the question say, how to explain an oscillator, and what's the must have for an oscillator?By physics-first, I mean explaining based on energy, causality, time domain and alike easy to grasp notions. Going from physics to math would be OK, the other way around, not so much.

author: IanB
author_rank: Super Contributor
timestamp: May 23, 2023, 01:39:00 pm
content: From a mathematical and physics point of view, you need to have a second order time derivative in the differential equation that describes the system. This is the only way the solution will include a complex exponential which will involve functions of sin() and cos().From an intuition point of view, the second order derivative will result from some concept of momentum in the system. Without momentum you cannot achieve oscillation.Momentum can be thought of as a form of energy storage due to velocity (call it "kinetic" energy). Oscillation is the result of energy cycling between storage as "kinetic" energy and storage as potential energy. If the losses in the system ("damping") are low enough, the transfer of energy back and forth between the "kinetic" and potential forms of storage can result in an underdamped or cyclic behavior.To make an oscillator you set up a system with cyclic (periodic) behavior, and then you feed in just enough energy to compensate for the losses, so that the oscillation continues indefinitely.

author: TimFox
author_rank: Super Contributor
timestamp: May 23, 2023, 01:54:52 pm
content: That is a reasonable description of an "harmonic oscillator". Note that any such device needs an external power source to maintain the oscillation.The prototype harmonic oscillator in physics discussions is a spring (force proportional to displacement) and a mass, where the position of the mass oscillates.Another oscillator type is the "relaxation oscillator", where only first derivatives appear in the analysis. A 555 or a neon bulb can provide the hysteresis that bounds the oscillation.

author: IanB
author_rank: Super Contributor
timestamp: May 23, 2023, 01:58:36 pm
content: I think even a relaxation oscillator would include a second order time derivative in its description (albeit hidden and very nonlinear). This is because a system containing more than one first order derivative can exhibit second order behavior (the converse is true also: a second order ODE can be decomposed into a paired system of first order ODEs).

author: CatalinaWOW
author_rank: Super Contributor
timestamp: May 23, 2023, 02:16:42 pm
content: Quote from: IanB on May 23, 2023, 01:58:36 pmThe relaxation oscillator highlights the fuzzy line between ideal models and reality. The conceptual oscillator can't be fully described by a differential equation because the trigger circuit is non continuous and has no meaningful derivatives. But it can be approximated mathematically and the physical reality can be matched by those approximations.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 23, 2023, 02:20:35 pm
content: Oscillator in the simplest physics sense (a passive oscillatory system e.g. spring-and-mass), or practically speaking (a driven system with feedback)? Or more specifically still, a combination of the two (a periodic or even ~sinusoidal oscillator)?A complete description to some very, very basic level, I think you'll have some trouble expressing, but if we say it's a given that atoms and molecules exist at around room temperature, then a basic chemical oscillator operating on a concentration gradient of reactants might be sufficient.Not sure offhand if there are simpler systems than that; perhaps some gas molecules have interesting enough dynamics that say a heat flux, or light, or excess kinetic energy (a molecular or particle beam?) is enough to induce oscillation. We could of course point to plasmas, but shall we include atomic transitions as instances of oscillation or not?There are molecular vibration modes that closely resemble a spring-and-mass system (quantum harmonic oscillator, QHO), wherein the energy levels are quantized, but the transition energy between adjacent states is approximately constant -- equivalent to the fixed resonant frequency of the classical harmonic oscillator. This is in contrast to the more sporadic modes of a bare atom for example, where similar dynamics might apply (with suitable stimulus (i.e., from its spectrum), we can increment between electron orbital levels), but not all states can be transitioned between, in a single event, due to spin selection rules. Whereas the QHO has a "ladder" state that allows free exchange of potential energy at the same frequency.From the more abstract side -- a linear ODE isn't sufficient description, as we necessarily have limited sources and sinks of energy/power. We can get nearly perpetual oscillators if we remove all influences; a lone planet in circular orbit of a lone star, pretty closely obeys such an equation, over time scales of billions of years (for suitable definition of "lone"); but not for all time, and eventually there will be significant exchange of energy with surrounding systems. (If nothing else, even for ideal rigid bodies orbiting in isolation from any others, gravitational waves will decay the orbit over heat-death time scales. Or maybe it's less than that? I forget.) Particularly for a driven system, we must include a logistic function that, given an input, limits maximum amplitude or energy exchange; and extraction, given an output. All real systems are nonlinear, having such a limit.More generally, we might specify an oscillator with a limit cycle, given some assumed energy input, exchange, and output. The 2nd order term might even be dominant (as in the above case), but other terms are necessary in a real system.The complexity then, is finding a way to express these terms, which is both simple enough to be useful, and real enough to be meaningful. I'm afraid I don't know enough about DEs anymore to help further with such a description. Anyway, the plan would be to start from a high level like this, and also from a low level (in whatever medium you like, be it fields, particles or combinations thereof), and meet in the middle with a complete description of an implementation/realization of that system.Assuming I've interpreted your meaning and intent correctly, of course!Tim

author: rstofer
author_rank: Super Contributor
timestamp: May 23, 2023, 03:20:53 pm
content: Quote from: IanB on May 23, 2023, 01:39:00 pmI really like this description. I have spent way too much time on the mass-spring-damper problem and analog computing to let this description slide by.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: May 23, 2023, 05:27:34 pm
content: The drinking bird toy is an example of a thermodynamic oscillator.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 23, 2023, 06:22:43 pm
content: Mostly it depends on how you define an oscillator.I generally consider an oscillator as something with positive feedback and gain greater than one, and thus an energy consuming processes. That is, you feed it with power and it produces an oscillating signal. This would include things like crystal oscillators, relaxation oscillators like a 555, drinking birds, lasers, and so on.But that excludes entirely passive things like spring/mass systems or LC circuits, which I would call "resonators". Resonator + gain + feedback => oscillator. It also excludes simple spinning objects like a pulsar which aren't (according to my general usage) either a resonator or an oscillator, it's just something that is periodic. This is consistent with the typical use in electronics where a bare quartz crystal is just called a "crystal", and a unit packaged with an amplifier is called a "crystal oscillator".But that's mostly a question of terminology, and how I use it. Other people in other contexts use those terms slightly differently. In physics, the specific phrase"simple harmonics oscillator" means any system with a second order linear differential equation. It can be driven, undriven, damped, or have the damping ignored. If you sharpen your question enough to be exact, the answer will probably be obvious.

author: westfw
author_rank: Super Contributor
timestamp: May 23, 2023, 06:25:34 pm
content: QuoteHow about a pendulum ? Or does the externality of gravity complicate things?

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 23, 2023, 06:34:27 pm
content: Quote from: T3sl4co1l on May 23, 2023, 02:20:35 pmAnd do we include more esoteric phenomena like quantumtime crystals, where the lowest energy state is a non-static, repetitive one?It all boils down to what you specifically and exactly mean by an oscillator. In my opinion, one useful disctinction is between the phenomenon, and as an usable tool._ _ _ _ _ _For the tool view, any sufficiently regular repetitive system whose phase space (behaviour with respect to any variable that may affect it) is such that useful amounts of energy can be exchanged (injected and/or extracted) without destabilizing the system, can be used as an oscillator.Basically all useful oscillators – all continuous-amplitude oscillators! – can be described as harmonic oscillators, damped harmonic oscillators, or driven harmonic oscillators. Even non-harmonic oscillators can be described as damped-driven harmonic oscillators, where the damping-driving force depends on the phase of the oscillator; with the base harmonic oscillator being a near approximation, with the damping-driving force causing only relatively small changes to the period and/or amplitude.The reasons for this are actually very interesting, and can be divided into two separate classes.One class is that any convex shape is analogous to a sphere. (There is a better mathematical term for this, but I can't recall it right now.) In the oscillator case, because we are interested in repetitive state changes, we care only about the interval at which the repetition occurs. So, whether nominal sub-states take an equal amount of time, does not matter. In essence, we don't care that much about the overall "shape" of the oscillation. (Insert automotive analogy about lap times with track of the same length but different shapes, or tracks of different length and shape but yielding same/similar lap times for each driver, here.)The other class is how any periodic continuous signal, say the amplitude of any continuous-state oscillator, can be decomposed into an (infinite) set of sinusoidal signals, and how even non-continous signals can be approximated to any desired precision: Fourier series. (Sine and cosine themselves being the solutions to any pure harmonic oscillator.)There is a third one, too: the smaller the amplitude compared to the energies and distances involved in an oscillator, the closer it seems to match a harmonic oscillator. However, I myself do not know why this is, or even if it is just a practical result of a noisy universe (i.e., any non-harmonic components drowned in noise in real life), so I consider it more or less just a rule of thumb.

author: IanB
author_rank: Super Contributor
timestamp: May 23, 2023, 06:40:03 pm
content: Quote from: CatalinaWOW on May 23, 2023, 02:16:42 pmThis is an interesting question. What is an "ideal model"? It is presumably a model where simplifications have been made to eliminate some less significant details and make it easier to work with. For example, texts on differential equations nearly always introduce the student to linear differential equations because they often permit an analytical solution to be obtained. But this is an idealization, since the real world is not often linear.In the real world beyond college and textbooks, complex systems are simulated numerically on a computer, and (possibly gross) nonlinearities in the system can be accommodated.For example, suppose you put an audio amplifier into a feedback loop by putting the microphone close to the speaker. The amplifier will saturate, the signal will clip like crazy, and the whole thing will be horribly nonlinear. Yet the system is made up of analog components that can be described with differential equations. There is undoubtedly no analytical solution, but a computer simulation if programmed sufficiently accurately could reproduce in a model what the feedback loop does in real life.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 23, 2023, 06:43:26 pm
content: The question started from an LC oscillator.At a first look, an oscillator would need an amplifier to substitute the lost energy, a limiter to keep the amplitude constant, and a positive feedback loop. Those alone won't cut it, would only make a latch. It needs some inertia/delay/memory (the LC tank in the starting example).This is where I couldn't decide what was the broader concept to pick. It can be a resonant oscillator as an LC, or it can be a forced oscillator with a comparator and something that flips the state, as in the drinking bird example.It gets even more bamboozling when thinking about numerical oscillators. What would mean energy conservation for a numerical oscillator, or momentum, or seeking minimum energy equilibrium, or inertia? All these are very important and inescapable in a physical oscillator, yet they don't make much sense, and they seem totally arbitrary for a numerical oscillator.That is why asking to identify the essential components of a physical oscillator, at first.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 23, 2023, 06:45:22 pm
content: Quote from: westfw on May 23, 2023, 06:25:34 pmNo, at least in my description / definition above a simple pendulum isn't any different. In that case, gravity is just providing the spring force. Now a pendulum clock has a mechanism to detect the motion of the arm and provide kicks, powered by a falling weight. That I would call an oscillator.

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 23, 2023, 07:23:56 pm
content: Quote from: RoGeorge on May 23, 2023, 06:43:26 pmYou end up with negative feedback. Which gives you a harmonic oscillator.When we include the "amplifier" and loss of energy, we get a damped-driven harmonic oscillator, where the damping is due to losses, and the driving matches the damping. Depending on the damping and driving mechanisms, they can cause a small change in the period.Note that while the amplitude of the harmonic oscillator depends on the energy involved, the period does not. So, small perturbations or fluctuations in the amount of damping or driving does not affect the period of the oscillator, as long as the amplitude stays within the elastic/ergodic range (where the same amount of energy that was needed to cause the change is released when returning to the original position) and the change is smooth and slow enough. Typically, the driving and damping are smooth and interdependent (matching each other intrinsically, both changing only slowly and smoothly, continuously, across multiple periods), so that their effect on the oscillator period is neglible, within environmental noise.Quote from: RoGeorge on May 23, 2023, 06:43:26 pmNumerical oscillators? Do you mean periodic functions and periodic sequences? They are based around periodicity, and from a physics perspective, they are "pure": more like empty universes than systems of interacting parts.

author: nctnico
author_rank: Super Contributor
timestamp: May 23, 2023, 07:25:34 pm
content: Quote from: RoGeorge on May 23, 2023, 06:43:26 pmThe way I see it is that in essence you'll need a 'body' that can resonate at a certain fundamental frequency. And then you'll need an energy source that provides energy to excitate the body to resonate at the fundamental frequency or a harmonic. The fundamental frequency is typically determined by how fast waves (electric, acoustic, pressure, etc) can travel through the body and bounce back from the edges.Even sea waves are a form of oscillation.

author: IanB
author_rank: Super Contributor
timestamp: May 23, 2023, 08:12:22 pm
content: Quote from: RoGeorge on May 23, 2023, 06:43:26 pmFor a harmonic oscillator the essential component is that the mathematical description includes some kind of 2nd order differential equation in time. With a first order system harmonic oscillation cannot happen.Another kind of oscillator results from switching, for example if you use logic elements to make a square wave. However, if you analyze at a small enough time scale even logic circuits are analog, and somewhere in the description will be 2nd order characteristics.

author: TimFox
author_rank: Super Contributor
timestamp: May 23, 2023, 09:06:56 pm
content: Quote from: westfw on May 23, 2023, 06:25:34 pmMy full statement was "The prototype harmonic oscillator in physics discussions is a spring and a mass."When you analyze the force on the mass (pendulum bob) due to gravity and the constraint of motion with a constant radius, you see a restoring force proportional to the sine of the pendulum angle, which for small amplitudes is extremely close to a force proportional to the angle itself. This gives the same equation as a mass connected to a spring, where the restoring force is proportional to the displacement (and reverses sign with the sign of the displacement).By the way, when you add "damping" to the simple harmonic oscillator, you need a damping force proportional to the velocity (also reversing with velocity). In a mechanical system, this is conventionally a "dashpot", which is the same basic device used in an automotive shock absorber. Friction does not have the ideal dependences. Such a damping force is analogous to the electrical loss (resistance) in an RLC electrical oscillator.

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 23, 2023, 09:22:26 pm
content: The only oscillators you cannot describe/approximate (to any desired precision) as some form or combination of (ideal/damped/driven) harmonic oscillator(s) are those based on actual physically discrete states, like certain quantum phenomena. Indeed, one second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 (133Cs).The duration of many quantum phenomena is surprisingly stable; they're just so darned short they're difficult to investigate.I'm not exactly sure what RoGeorge meant by numerical oscillators, but all practical use cases I can think of relies on either discrete states or discrete time variable steps, so they're better modeled as periodic systems with either discrete states, or discretelysampledstates instead.For example, in Conway's Game of Life, there are a number of periodic patterns, both static and moving. In many ways, these can be considered time crystals: their base state is not a single state, but a sequence of discrete states, that proceeds without interaction or any transfer of energy.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: May 24, 2023, 01:38:01 am
content: Quote from: IanB on May 23, 2023, 06:40:03 pmThere is a language problem here. Ideal vs idealized. Ideal in the way you used it means best, or optimum or most useful. Which in different situations can mean simplest or most accurate or cheapest to execute. Idealized in the sense I meant is more in the sense of prototypical. An idealized square wave has zero rise time. And can be approximated to any desires accuracy by a series of harmonic oscillators. But never exactly recreated. So technically this square wave isn't the solution of a differential equation. But I am an engineer and the harmonic series are close enough.

author: rstofer
author_rank: Super Contributor
timestamp: May 24, 2023, 01:39:44 am
content: Attached is a MATLAB/Simulink simulation of a mass-spring-damper. If the D terms goes to 0, it is an oscillator.The solution is based on the work of Lord Kelvin. Basically, we assume we have y'' (but we don't yet) and integrate it to get y' and then integrate again to get y. Now we sum up the scaled values to create y'' and stuff it back in the input (now that we actually have it). This is the genius of analog computing; integrate until you get rid of the derivatives. Notice the IC=-1 term adjacent to the second integrator. It sets the initial condition to -1.But, as stated above, you need a second order equation to get oscillation.

author: thermistor-guy
author_rank: Frequent Contributor
timestamp: May 24, 2023, 03:38:17 am
content: Quote from: RoGeorge on May 23, 2023, 01:00:33 pmOscillation in what domain, exactly?Predator-prey populations can oscillate.Many organisms have a sleep-wake cycle, and this is old in evolutionary terms:https://www.caltech.edu/about/news/surprising-ancient-behavior-jellyfish-79701There is a long cycle in human affairs. We are currently in the cycle phase called "The Fourth Turning"https://en.wikipedia.org/wiki/Strauss%E2%80%93Howe_generational_theoryWhen you say "physics first", I assume you are reaching for something fundamental to alldomains where oscillation occurs. Are you aiming the question at electrical and mechanicalsystems only?

author: Brumby
author_rank: Unknown
timestamp: May 24, 2023, 03:46:10 am
content: My first thought was: Build an amplifier.

author: IanB
author_rank: Super Contributor
timestamp: May 24, 2023, 04:09:07 am
content: Quote from: CatalinaWOW on May 24, 2023, 01:38:01 amI was using ideal in exactly the sense you described, to mean idealized or perfect. So I would say that an ideal or perfect square wave model has been simplified to remove such imperfections as finite rise time, or overshoot, that inevitably occur in the real world and that do not need to be considered for many purposes.

author: IanB
author_rank: Super Contributor
timestamp: May 24, 2023, 04:15:46 am
content: Quote from: thermistor-guy on May 24, 2023, 03:38:17 amIt doesn't really matter, due the principle of analogous systems. It turns out that if you construct a mathematical model starting in any given domain, and then reduce it to dimensionless form, you generally end up with the same model to describe the same kind of system behavior.

author: bdunham7
author_rank: Super Contributor
timestamp: May 24, 2023, 04:16:25 am
content: Take a Geiger counter and connect the output, with appropriate buffering, to a clock divider circuit like the ones that divide down a 32768Hz crystal oscillator, set up to put out a 1Hz 50% duty cycle square wave. Now put the Geiger counter in a box along with a gamma-emitter like Cobalt-60 and adjust the sample position until you get approximately a 1Hz output from the divider circuit.Is that an oscillator?

author: IanB
author_rank: Super Contributor
timestamp: May 24, 2023, 04:21:11 am
content: Quote from: bdunham7 on May 24, 2023, 04:16:25 amWell, that would depend on how you wish to define oscillator.But in a physics sense, there is no feedback, no momentum effect, no second order dynamic behavior of the process.It would seem more like a random number generator.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 24, 2023, 08:20:12 am
content: Quote from: Nominal Animal on May 23, 2023, 07:23:56 pmSomething like that. That type of question comes from an email "debate". At some point I was trying to look at the behaviour of a (physical) band-pass filter as a variable impedance, where the energy at the filter input will be reflected back (when the input impedance does not match), or transferred to the output. Probably a wrong way to look at a filter, it was about switched filters and in another context, anyway,TL;DR, the other guy asked "if you say a filter is an impedance mismatch reflecting back some input energy, then what is reflected back in a numerical filter, like a DSP?".I should have stay to physical oscillators only, and not mention the numerical implementations, that's another talk entirely, sorry.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 24, 2023, 09:00:24 am
content: Quote from: IanB on May 23, 2023, 08:12:22 pmFor mathematicians, derivatives can mean a lot of things and do many tricks. To me, less skilled with math, first derivative means the slope of a plot, or speed in mechanics. And the second derivative means to me the curvature of a plot, like acceleration in mechanics. I prefer thinking rather in physical terms, like speed and acceleration, because it's something that can be directly experienced by everybody.So, if I try to translate 2nd derivative in words, would it be correct to say an oscillator needs some sort of acceleration in its behavior? If yes, then a rotating disk would also be an oscillator. This might still be OK (saying "might" because just like ejeffrey, I'm tempted to think circular motion is not the same as an oscillator), but the 2nd derivative condition doesn't make any good if, for example, it's a linear acceleration. Something has to repeat, to be periodic, to alternate. I don't see how the 2nd derivative implies alternation, or am I misunderstanding the 2nd derivative condition you were mentioning?To me, the problem of explaining something in terms of math is that there is no causality in an equation. An equation is an equivalence, a relation between it's terms, and that can only be true or false. It's like saying an oscillator is something that satisfy the oscillating conditions. That would be a circular definition, same as saying an oscillator is an oscillator.I'm not dismissing your explanation, only trying to say what I didn't understood, or what difficulties I have with it.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 24, 2023, 10:06:32 am
content: Quote from: westfw on May 23, 2023, 06:25:34 pmWe could do some interesting categorization with respect to the decay mechanism (or conversely, gain when applicable). Note that simple rotation decays over time, resulting in a reduced frequency. That's a very nonlinear sort of behavior compared to SHM. Depending on the loss mechanism, the decay might be exponential, or double-exponential or something else (compare constant frictional resistance vs. friction proportional to angular velocity*). Or it might be increasing, with a hyperbolic decay curve -- as for an orbital system (frequency ~ 1/energy) decaying under gravitational radiation.*Well... there was a kernel of something more interesting in my mind, but it doesn't sound very special when written out, does it? Simple resistance is torque proportional to angular velocity, which gives a simple pole (exponential decay), the usual case. But there are mechanisms which are strongly dependent on rotation rate, or frequency (in quantum terms, E ~ ν, but the emission / coupling rate matters too, and I don't know offhand any figures for that), or say temperature (radiation ~ T^4).Say we stick a magnet or battery to the rotor, so it's emitting EM waves at the rotation frequency; at most frequencies, it will be a short dipole so loss varies strongly with frequency. (Ah, but does it vary proportionally, or square law, or more? I don't recall offhand**.)But these are more easily collected by specifying an amplitude- or rate-dependent function, and observe the special cases for loss = 0 (perpetual) and loss ~ rate (constant resistance), then solve for whatever the resulting decay curve is (or infer the opposite way just as well).**Well, induced voltage (relative to a non-rotating reference frame) is proportional to rate, and, what, a short dipole has radiation resistance as 1/λ^2? Which will be the series equivalent resistance of the lossy capacitor, so...V ~ ωI ~ V / Xc ~ V ω ~ ω^2λ ~ 1/ωR ~ 1 / λ^2 ~ ω^2P ~ I^2 RP ~ ω^6 ??Quote from: Nominal Animal on May 23, 2023, 06:34:27 pmGaussian curvature..?QuoteIn general that's just linearization around a point; in this case, a small cycle around phase space. If the system is continuous, it approximates a SHO orbit.I suppose for certain dynamic systems, we can employ transformations to convert limit cycles into limit points, and map non-circular trajectories onto unit circles (thus accounting for harmonic distortion). The existence of such a mapping, on a given system, might suggest its generalized-SHO-ness.Quote from: RoGeorge on May 23, 2023, 06:43:26 pmNCOs are abstracted in a different direction: an iterated transformation (discrete-time) on a discrete state vector (i.e. bits in memory). We could indeed apply some implementation (whether transistors or otherwise), assign an energy or power cost to the states, or transitions therebetween, and model it the same way -- just with a lot of extra steps.More tantalizing, I suppose, might be applying such maps as above -- suppose we implement an NCO using "lossless" digital logic, at such a clock rate that the loss tangent of the capacitances is sufficiently negligible, and using an LC oscillator (and whatever applicable phase-shift networks) to afford the various clock phases required for operation. Then we could have a digital description of a continuous oscillating system, which exhibits rather complex behavior (various period-multiplication effects as the counters roll over from time to time) but overall is nonetheless, not just coherent with, but indeed energetically coupled to, our reference oscillator.The standard implementation today is very much more mundane; since our information-theoretic efficiency is piss (something like ~10^6 times more energy loss per bit transformation), it's basically a class A amplifier: all power dissipation all the time. And with all that wasted power, it really doesn't matter what happens. You have the space for a lot of complicated -- but thermodynamically irrelevant -- functions.Tim

author: IanB
author_rank: Super Contributor
timestamp: May 24, 2023, 03:20:07 pm
content: Quote from: RoGeorge on May 24, 2023, 09:00:24 amYes, but more precisely momentum, or transformation of energy between kinetic (relating to movement) and potential (relating to position) forms.QuoteNo, if it is simply rotating freely on a spindle. Yes, if it involves energy transformations between movement and position (a balance wheel in a watch).QuoteYes, the second derivative enables alternation, but does not guarantee it (there can be overdamped systems).A second order term is needed for oscillation, but not all second order systems will oscillate.QuoteAn equation if properly constructed is a mathematical model of a physical system. It replaces intuition with analysis, and enables predictions to be made about how the physical system will behave. If you write a good model of a system, you can tell if the system will oscillate.

author: bdunham7
author_rank: Super Contributor
timestamp: May 24, 2023, 03:33:52 pm
content: Quote from: IanB on May 24, 2023, 04:21:11 amPerhaps there the terms 'resonate' and 'oscillate' should be contrasted and compared here. A relaxation oscillator seems to not quite fit some of the definitions of 'oscillator' that I'm seeing discussed here. The only difference I can see between my proposed device and a relaxation oscillator is that the latter works by the accumulation of physical energy and the former accumulates a record of the energy. You could redesign things so that each pip of the Geiger counter would add a small charge to a capacitor until a neon bulb discharges it. Would that be different?QuoteIf it were a black box, how would you describe it based solely on it's output?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 24, 2023, 03:56:49 pm
content: Quote from: IanB on May 24, 2023, 03:20:07 pmWhy so chauvinistic about kinds of energy transformations?Free rotation being the exchange of linear kinetic energy between orthogonal axes. The state variable and conjugate are position and position (or velocity or whatever). It bears all the other hallmarks, like centripetal force implying energy storage (and indeed storing a little in the material elastically, though usually not enough to worry about).I understand the feeling though. It seems too trivial or simple a form.Tim

author: westfw
author_rank: Super Contributor
timestamp: May 25, 2023, 01:55:17 am
content: QuoteCertainly any point on the disk (except the center) appears to oscillate in nice sinusoids on any one-dimension axis.I'm not sure how that ties in to the need for energy transfers...

author: RJSV
author_rank: Super Contributor
timestamp: May 25, 2023, 02:16:11 am
content: Dealing with low level logic, the essential 'work horse' concept is the simple inverter, allowing for some complexity in the time domain, with certain hookups (or topography).So, skipping the complexities of integrals and differentials, is just a few logic gates, and time delays in propagation, AN OSCILLATOR can be had, and can be described, inside a 'paradox' structure. For the particular paradox, being harnessed, your oscillator needs to be under two rules:#1.). Output follows input logic level, with perhaps optional gain.and"2.). Input is generated by processing output through an inverter, where both signals are digital, or two state having thresholds for switching requirements.I think that's a logic defined oscillator, vs. the analog definitions seen in some replies here.

author: jwet
author_rank: Frequent Contributor
timestamp: May 25, 2023, 02:40:04 am
content: Okay - here are the definitiive answers* to all these questions-The radioactive decay example isn't an oscillator. It is a sensor measuring a random natural process which isn't oscillatory- doesn't repeat and has no period.Taking a component of rotary motion is an oscillator whether with a crankshaft, cam or balance wheel cogging effect. A rotating disk alone is not an oscillator.NCO's are not oscillators- they are summers, they require an oscillator to operate*- I'm being facetious of course- there are thousands of these kind of stipulated functions that we use every day. I think its best not to think about them too heavily lest you get sucked into your naval.

author: SiliconWizard
author_rank: Super Contributor
timestamp: May 25, 2023, 03:52:01 am
content: To answer "what's the must have for an oscillator?", I think the most basic answer would be: any system that can have at least 2 states, and some energy. One may reply to this that any physical system that can have more than 1 state implies the presence of energy, so that would simplify to just: some energy.

author: thermistor-guy
author_rank: Frequent Contributor
timestamp: May 25, 2023, 04:58:41 am
content: Quote from: Brumby on May 24, 2023, 03:46:10 amOr a switch-mode power supply.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 25, 2023, 08:42:40 am
content: Quote from: SiliconWizard on May 25, 2023, 03:52:01 amNMR "rings a bell"Quote from: thermistor-guy on May 25, 2023, 04:58:41 amClass D is still an amplifier for a reason.Tim

author: RoGeorge
author_rank: Super Contributor
timestamp: May 25, 2023, 11:15:56 am
content: The question originated from an analog oscillator for RF.Maybe the oscillator's definition should be narrowed down a little:- physical device- has an external power source as its only input (any constant DC-like power input, but not necessarily electric power)- can output a sustained oscillation (of constant amplitude)- by oscillation, it means a periodic waveform, with a predictable shape and frequency (not chaotic-attractors based oscillator, or alike)- doesn't need other internal clocks/oscillatorsA spring+weight can oscillate, but it's not an oscillator because it's not constant amplitude. A digital counter, also not an oscillator because would need an external clock, and so on.

author: DiTBho
author_rank: Super Contributor
timestamp: May 25, 2023, 11:21:51 am
content: this is as simple, as interesting

author: DiTBho
author_rank: Super Contributor
timestamp: May 25, 2023, 11:31:47 am
content: @RoGeorgeI think a good answer comes from theBarkhausen Criterion. It says the principle of the oscillator is that when the feedback factor or the loop gain is one, then the overall gain of the oscillator circuit will be infinite.So you have blocks, equations in both time and frequency domains, a lot of material, and a criterion!

author: IanB
author_rank: Super Contributor
timestamp: May 25, 2023, 01:28:31 pm
content: Quote from: RoGeorge on May 25, 2023, 11:15:56 amWhat about the movement in a mechanical watch or clock? That contains a spring+weight oscillator that has constant amplitude.External power input is a given for anything that is not a perpetual motion machine.

author: TimFox
author_rank: Super Contributor
timestamp: May 25, 2023, 03:11:07 pm
content: Quote from: IanB on May 25, 2023, 01:28:31 pmThis was supposed to start with physics.In any freshman physics textbook, discussion of "simple harmonic oscillators" starts with the mass and spring, then we add an external force to get the "forced harmonic oscillator" to understand resonance phenomena, then we add damping to get the "forced damped harmonic oscillator" to understand the frequency response of such an oscillator with explicit energy loss during the oscillation.The differential equations used in this development then appear in the analysis of analogous oscillators.In engineering, we then look at "feedback oscillators", where the basic oscillator (e.g., RLC circuit) governs the timing of a packaged circuit to generate a continuous oscillation from an external power source.

author: jwet
author_rank: Frequent Contributor
timestamp: May 25, 2023, 06:28:44 pm
content: Barkhausen doesn't cover relaxation oscillators. Make an RC cicuit, connect it to a 100v source, the C will charge up, now, put a neon bulb across the cap, it will trigger at 70v discharging the cap and keep going. You could make a strained argument that the neon lamp has negative resistance which is gain etc, but this isn't how it operates really.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 25, 2023, 07:04:04 pm
content: I should have wrote self-sustained oscillator, or generator. An entire mechanical clock is OK as a generator.Nothing wrong starting with spring+weight, just that those two alone can not produce sustained oscillations. They will need more component blocks around the spring+weight, so to replace the lost energy such that the amplitude and the frequency remain constant.I'm tempted to say there are two different mechanisms to keep all in check:- one is by comparing the amplitude with some reference value, like in an RC oscillator- the other is by comparing current value with previous value of itself, like in a LC oscillator or alike harmonic osc

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 25, 2023, 07:16:34 pm
content: Quote from: jwet on May 25, 2023, 06:28:44 pmTry it at 100kHz and tell me it's not negative resistance.To put a more subtle point on it -- it can still obey the criteria locally (i.e. for small signals around a turning point), while being nonlinear enough overall to not seem to operate that way ("latches on and off"). Or we can tweak operation towards corners of operation (in this case, at frequencies approaching the deionization time of the plasma) to get a smaller amplitude that more closely approaches the linear conditions we expect for such a system.Though, keep in mind here too, there is nonlinearity: it may be oscillating, but it's at a low amplitude; what's setting that amplitude? Presumably there's a negative resistance driving oscillation, but there's a dependent positive resistance that competes, limiting amplitude.Tim

author: RoGeorge
author_rank: Super Contributor
timestamp: May 27, 2023, 08:02:13 am
content: Any clues why the energy goes back-and-forth between two forms of storage? This time asking for the resonator only, without the amplifier or the feedback needed to sustain the oscillations indefinitely.For example, why the energy changes back and forth between potential and kinetic in a mechanical resonator, or between its electric and magnetic forms in an LC resonator?

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 27, 2023, 01:34:08 pm
content: Quote from: RoGeorge on May 27, 2023, 08:02:13 amBecause of the structure of the system.Put snarkily, "If it didn't, it would notbeone."Take a look at potential and kinetic energy in a frictionless 2D pendulum, limiting the angular deflection \$\theta\$ to small angles where \$\sin \theta \approx \theta\$ (small-angle approximation, also simplifies the pendulum to a harmonic oscillator), and assuming all the mass \$m\$ is at distance \$\ell\$ from the pivot point (massless rod between pivot and the tip). If origin is at equilibrium position, vertical displacement \$h = \ell (1 - \cos \theta)\$, and horizontal displacement \$x = \sin \theta\$, and the pivot point is at \$(0, \ell)\$. As an isolated frictionless system, total energy is conserved, and therefore the sum of potential and kinetic energy is constant. You'll find that it is the physical geometry of the pendulum thatforcesthe total energy to swing between potential and kinetic energies, because you can derive thewhyof the swinging just from the structure, starting from any positive total energy initial point.For a true simulation of a pendulum, we need to solve the differential equations of motion numerically because no simple algebraic solution exists. We can do that to any precision we want, and the solutions do converge within all physically sensible initial conditions, even when we model the pendulum itself as a physical object (both continuous matter and "atoms" of interacting particles) in 3D, including the expected difference in oscillation period between the above simplified model (harmonic oscillator) and true pendulum. So, it is definitely the structure of the pendulum itself that causes the oscillation, not some external principle or cause or rule.

author: TimFox
author_rank: Super Contributor
timestamp: May 27, 2023, 01:44:34 pm
content: For the spring and mass simple harmonic oscillator (ignoring damping), we start with an initial condition, where the mass is at rest, displaced to positionxIaway from the equilibrium positionx= 0.Before releasing the mass, all the energy is potential energy of the spring,V= (1/2)kxI2, wherekis the spring constant (Hooke's Law) in N/m.When the mass is released, the "restoring force"F= -k xfrom the spring will accelerate the mass back towards equilibrium, but when it goes past equilibrium it is moving with a finite velocity and goes past the equilibrium position (x= 0).Atx= 0, there is no potential energy left in the spring: it has all been converted to kinetic energy of the massT= (1/2)m v2.Proceeding past equilibrium, the restoring force decelerates the mass until the velocity and kinetic energy reach 0, and all the energy has been converted back to potential energy in the spring.We then proceed into the second half of the first cycle, as the mass accelerates back through equilibrium position until it reaches the initial position (no energy loss in this example), stops, and the motion reverses to start the first half of the second cycle.Etc.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 27, 2023, 03:22:15 pm
content: So, it's the particular arrangement of a given set of rules, plus the interaction between them, and that makes a certain behavior to emerge.In the physical world, the set of rules would be the laws of physics. And to make a particular arrangement out of them, it usually means to put some in close proximity, such that those laws will be interacting with each other. There's so much to speculate in this direction.The idea of everything taken as emergent behavior feels like an epiphany, because until now I was considering as emergent phenomena only theappearanceof something that it is not really there, for example a bank of fish being "repelled" by a predator.

author: TimFox
author_rank: Super Contributor
timestamp: May 27, 2023, 03:34:38 pm
content: In physics, the harmonic oscillator in its various forms (simple, damped, forced, coupled, etc.) is fundamental to many other phenomena, and freshman physics concentrates on it accordingly.Often, analyzing such systems in terms of energy is easier to understand than an analysis in terms of forces, but the physical results are the same.In advanced classical physics, the Hamiltonian re-formulation of Newtonian mechanics is a very powerful tool to deal with more complex systems with many degrees of freedom, defining a "generalized co-ordinate" and "generalized momentum" for each degree of freedom (which may not be perpendicular to each other), and later work used the Hamiltonian approach for quantum mechanics.A good senior-undergraduate textbook for such topics is by Goldsteinhttps://physicsgg.files.wordpress.com/2014/12/classical_mechanics_goldstein_3ed.pdfSee Chapter 6 for a detailed description of oscillation.(When I purchased the first edition back in 1969, I believe it cost $17. Much later, I purchased the third edition for approximately $110. The above link is a downloadable huge pdf.)

author: CatalinaWOW
author_rank: Super Contributor
timestamp: May 27, 2023, 04:00:29 pm
content: Quote from: RoGeorge on May 27, 2023, 03:22:15 pmYou are in some deep philosophical ground there. Newton's laws, the spring constant relationship and other rules are our description of how the system works. We like the description because it matches behavior. But I don't think the rules make the system. The system is, and happens to conform to some degree to a set of rules we have constructed. We may or may not understand the underlying system.The most common example to make this point clearer is the use of epicycles to describe the motions of heavenly bodies in a geocentric model of the cosmos. These rules actually worked quite well, and described the behavior of the visible bodies in the sky to the limits of observational accuracy for millenia. It wasn't until about 500 years ago when the very detail measurements of Tycho Brahe started to show discrepancies with the simpler epicycle models. And more complex epicycle models were constructed to explain the new data. Today most would agree that actual reality doesn't conform to these sets of rules.The glib answer to your question of why the energy transfers back and forth is because nothing is stopping it. If you connect a charged capacitor to an inductor what is stopping that charge (and hence the stored energy) from flowing through the inductor? In this case the inductor puts up a bit of a fight, generating a counter voltage - the back emf - proportional to the change in current. But it only slows, does not stop the flow. At some point the voltage on the capacitor drops below the back emf and the sign of the current change reverses. Now the inductor is pulling charge out of the capacitor to prevent instantaneous magnetic field collapse. Which continues until the field reaches zero, where it turns out that all of the charge has returned to the capacitor.Same exact situation as releasing a mass attached to a stretched spring. Nothing is stopping the mass from moving so the spring has its way. For a while.

author: jwet
author_rank: Frequent Contributor
timestamp: May 27, 2023, 04:46:13 pm
content: Quartz crystals also have this bouncing feature- strain to electricity, electricity to strain. Its not a necessity of the physics but it does make for an "efficient" oscillator.

author: TimFox
author_rank: Super Contributor
timestamp: May 27, 2023, 05:15:15 pm
content: An interesting difference between resonators such as quartz crystals and simple oscillators (mass and spring) is that resonators can have multiple resonant frequencies, while simple oscillators have only the one.One-dimensional resonators (organ pipes, violin strings, resonant transmission lines, etc.) have harmonic overtone frequencies (integer multiples of the lowest or fundamental resonant frequency), but three-dimensional resonators (quartz crystals, resonant cavities, etc.) have overtones that are not harmonic frequencies.

author: AndyBeez
author_rank: Frequent Contributor
timestamp: May 27, 2023, 05:19:00 pm
content: Quote from: westfw on May 23, 2023, 06:25:34 pmOr a planet orbiting a star? Velocity relative to the star comes out as a sine wave... of sorts. Also electrons orbiting the nucleus too. For a pure audio sine wave, how about the physics of a tuning fork? Really, everything is in oscillation. Or resonating. Except for that RF oscillator you designed and spent hours building

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 27, 2023, 05:48:40 pm
content: Quote from: TimFox on May 27, 2023, 05:15:15 pmSort of. Several of these are dispersive so have nonharmonic overtones. Acoustic resonators are a good example, or better to say: acoustic waveguides. Most waveguides I suppose, share this property?Bulk material vibrations are especially rich, having three directions each longitudinal, transverse, and shear, all with different wave velocities, all which couple to each other to varying degrees depending on geometry (and in nonlinear combinations, because displacement determines the moment on which longitudinal force acts, etc.).EM structures with interaction between nearby elements (not just directly adjacent) also works. Consider the helical waveguide for example.Or for more quantum examples, consider the 1/n^2 spectrum of atomic levels; the resonator is highly irregularly shaped (a spherical 1/r potential well) so different states have very different waves. At least until you get to the Rydberg sort of levels where states (or modest superpositions thereof) start to look like classical orbits.Tim

author: TimFox
author_rank: Super Contributor
timestamp: May 27, 2023, 07:26:49 pm
content: Also, in the classical simple harmonic oscillator, obviously the minimum possible energy stored in the system is zero, where the displacement and velocity are both zero.In quantum mechanics, such a state violates Heisenberg, since both the position and momentum are zero, with no uncertainty.In the quantum harmonic oscillator (a prototype for many physical systems), the minimum state is given byE0= (h f)/2 , wherefis the natural frequency of the oscillator andhis Planck's constant.and the discrete set of energies is given byEn= (n+ 1/2)h ffor non-negative integersnThe spacing between these states ish f(This is usually written h-bar omega, but I'm too lazy for proper typesetting.)

author: TimFox
author_rank: Super Contributor
timestamp: May 27, 2023, 07:30:12 pm
content: Separate issue about overtones and harmonics:Sometimes people confuse the harmonic frequencies of a simple (non-dispersive) one-dimensional system (such as a violin string) with the harmonic frequencies that appear in the Fourier series for the decomposition of any periodic waveform.They have the same form (integer times fundamental frequency), but originate differently.

author: AndyBeez
author_rank: Frequent Contributor
timestamp: May 27, 2023, 07:39:07 pm
content: ...and ring modulation

author: jwet
author_rank: Frequent Contributor
timestamp: May 27, 2023, 07:43:48 pm
content: Further down the rabbit hole...I worked on what was to be "the lowest power" Real Time Clock project at Maxim a while back. Maxim was big on superlatives and did a lot of projects like this- we called them "10x" projects where you blew some important spec out of the water by 10x or more. I was the product definer- an apps engineer that works with design to understand the need fully, nail down specs, often interview customers and do market and technical research. One of things that came out of this for me in a philosophical sense was that its "impossible" to keep time without using energy. Anything that keeps time uses energy, I thought this was interesting if not profound. We delivered a 200 nA RTC- DS1302. The world record today is held by the MAX31331- taking only 65 nA to keep time! There are real needs for sub sub 1 uA clocks believe it or not.

author: thermistor-guy
author_rank: Frequent Contributor
timestamp: May 29, 2023, 01:41:41 am
content: Quote from: TimFox on May 27, 2023, 05:15:15 pmSpeaking of three-dimensional resonators: the earth-ionosphere cavity, excited by lightning:https://en.wikipedia.org/wiki/Schumann_resonances

author: metebalci
author_rank: Frequent Contributor
timestamp: May 30, 2023, 06:33:02 am
content: A physics-first approach is asked, but I guess I am not a physics person, and I think about oscillations often in terms of dynamical systems recently. So I guess one needs a proper configuration of one or two fixed points, or a limit cycle or a strange attractor for oscillatory behavior. The behavior of latter two may quickly become weird so not many practical electronics applications I guess, other than sound/noise generation maybe.

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 30, 2023, 10:33:46 am
content: Quote from: RoGeorge on May 27, 2023, 03:22:15 pmYes. Cellular automata, especially Conway's Game of Life, is a good way of experimenting with this. If you like combining low-level programming (large world, bit per cell) and user interfaces (viewing the world at 1:1 or more than one cell per pixel), even more so. You can adjust the rules, including extend the grid area involved, add directional weights, et cetera. Even with the Conway's trivial ruleset, it is Turing-complete: there are enough emergent behaviour that any Turing machine (computer) can be simulated.Simulating even simple microprocessors takes huge numbers of cells, and therefore clever optimizations to compute the cell states efficiently; yet, it is always only the simple rules being implemented. (It is also an interesting exercise in examining the rules themselves: sometimes some simple rule is very difficult to implement, whereas some complex rule can be trivial to implement. We cannot really tell, until we attempt to implement the rule, somehow, first.)Quote from: RoGeorge on May 27, 2023, 03:22:15 pmThis is exactly how "vague" language can constrict thought, and why mathematics is so useful in describing the rules and behaviour.Some insist that mathematics is not a language. Perhaps so, but it definitely can be used as one to describe these things.The true "trick" is correctly and efficiently translating between math and human understanding, especially human intuition.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 30, 2023, 06:47:05 pm
content: Spoken language may be too vague, while mathematics can be too exact, either of these extremes can be less productive.Math is a great tool for crunching relations/abstractions, similar to how computers are good at crunching numbers. Though, it is too exact to let room for any serendipity. Serendipity helps a lot when exploring.I don't see mathematics as a seeking tool. Only using it occasionally, as a confirmation tool to check if an idea is correct, or as a dismissing tool, to get rid of those too seductive hypotheses that stick to mind.Then, I don't know enough mathematics. It's hard to learn, hard to handle, mistakes are easy to make but hard to spot, it is crucial to properly encode, then decode/interpret the results, etc.Most of all, it's an axiomatic system, that started from the real world. Remember it all started from counting the sheep and measuring the land. That also means it will not work outside its axioms. There are always tacit assumptions, even in math axioms. Having in mind the way geometry started from measuring flat agriculture land, and that led to Euclidean geometry. If axioms are even slightly modified, we get new theorems and new mathematics, like the non Euclidean geometry. Not a big deal now, looking in perspective, but a big deal if back then one would try to use Euclidean geometry to prove/disprove some non Euclidean hypothesis. One would have get a big no, because of using the wrong set of axioms.I guess these are all epistemology 101 and studied systematic there, though I never managed to follow any book or lectures about epistemology, looked very outdated. I see human mind as a fuzzy lookup table, where the lookup table entries were filled up in the very early years, with notions we learn by interacting with the world. Those are the basic concepts in which we understand everything else. Later we learn to associate the most common entries in our lookup tables with words. Filling the table happens in the very first years of life, before self-awareness emerges. The table will keep updating for the rest of the life, but at a much slower peace. When a fact matches very well the lookup table entries, we are in the ordinary, expected, or maybe boring situations. When we encounter something for which we don't have a matching entry yet, we tend to reject that, or to take it as a "mind-blowing" new something.All we do, and feel, and think is in terms of our inner lookup table,plus some internal noise. The inner lookup tables being fuzzy and noisy, can sometimes lead to unexpected behavior or to creativity.Sounds a lot like tokens from ChatGPT, but the fuzzy lookup tables idea came to me from hardware, not software. I've start playing with the lookup table analogy a couple of decades ago, probably inspired from the FPGA architecture, where everything is a lookup table.Even funnier when it comes to awareness. I think what we call self-awareness is the ability of computing assisted-simulations of the world in which we live in, based on two things:- the already existing entries in the fuzzy lookup tables- the live sensory input data stream we have from our sensesBy assisted-simulation, I mean the projections of the outcome is based on the lookup table, and the sensory input is used as a feedback. Sensory input (e.g. vision, hearing, tactile, etc) is what we compare against, in order to check how accurate the prediction/simulation was. Then adjust the simulation accordingly. If we are left out without any sensory input, we start hallucinating (e.g. when sleeping, or under certain drugs, or in isolation tanks).In fact, the more advanced an animal is in the tree of life, the more aware and the more capable is at computing the surroundings. Reaction times are very slow, so animals got themselves good at predicting the future. I believe our day to day life is a living simulation, a dream that is continuously adjusted, adjusted such that the simulation won't diverge too far from the sensory input stream.We navigate reality, and react to what our mindpredicted, rather than to what our senses read back from the environment.Sorry for going with the flow with the offtopic, it's hard to be concise and convincing at the same time. All these might be as well nothing but too much noise in the lookup tables.Not trying to dismiss math, mathematics is a must have for rigorous work. Though, when seeking/exploring at leisure, I found handling concepts from that fuzzy lookup table more fun to work with than math. It's way faster to process inner thoughts, and more productive at generating new ideas. Then triage later which ones may worth investigating further.Many such generated ideas will be way off, and the internal lookup table keeps updating according to what it is exposed-to the most (that's a pitfall of our inner working, learning is always on, so a lie repeated a thousand times becomes truth). So it's a risk that, eventually, some of the false ideas generated by words instead of math will be assimilated as truth in the own lookup table. And just like that, one might start wearing pointy hats and pretend to be Napoleon.That's why one should never skip the mathematical proof.

author: HuronKing
author_rank: Frequent Contributor
timestamp: May 30, 2023, 07:48:31 pm
content: On the subject of mathematics as descriptor though - I am heavily persuaded by the fact that mathematical constructs have led us to predicting and discovering pretty bizarre phenomena in nature - like the positron.Like, really, how crazy is that?"Here is this equation that describes this quantum phenomena... and when we follow the math to its conclusion - it tells us that positively charged electrons should exist. And they do exist!"Amazing.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 30, 2023, 09:02:06 pm
content: Indeed, one can discover by observing mathematical results. It is even possible to make discoveries by crunching numbers (by simulation). And in the recent years there are more and more papers with discoveries made by AI exploration.What bothers me is that they all fail to explain why something happens.Would be great to have a new type of mathematics, with embedded causality in it.

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 31, 2023, 05:02:36 am
content: Quote from: RoGeorge on May 30, 2023, 09:02:06 pmThat is because we can only describe how, not why, in any language. Even physics don't tell you why, only how.I suspect 'why' is outside the scope, and belongs to philosophy or religion; one of those axiomatic things that are unprovable from the results/observations, which is all we have.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 31, 2023, 06:42:27 am
content: The kind of "why" I am missing is not the philosophical one. Only seeking to explain the sequence of events, what causes something to happen, or to manifest itself.By explaining, I mean identifying the irreducible basic components that are needed for something to happen. The choice of what would be considered as basic components is not important. Can be the binary 0/1 from information theory, or the water/fire/air/earth, or any other choice, as long as they can be consistent along all the observations we can make in our physical world.The idea of irreducible laws of physics (or infinite complexity), or the idea that time doesn't exist, seem more like theoretical speculation. I see structure and causality everywhere, plus some progress with physics unification.

author: IanB
author_rank: Super Contributor
timestamp: May 31, 2023, 06:59:00 am
content: Quote from: RoGeorge on May 30, 2023, 09:02:06 pmIf you start out with a simple harmonic system like the mass and spring with damping, then write down the equation that describes it from first principles, you will find that for certain parameter values the solution to the equation contains a term like sin(wt), meaning that it will oscillate. This sequence of steps from analysis to solution explains exactly why it oscillates in the best manner you will obtain.If you want an intuition about the solution, you can consider what happens if you pull the mass away from the resting position and let it go. If, when the mass returns to the resting position, it is still moving, then it will oscillate. If, when the mass returns to the resting position, it has stopped moving, then it will not oscillate.QuoteThere is already such a type of mathematics. It is called physics.

author: Nominal Animal
author_rank: Super Contributor
timestamp: May 31, 2023, 08:27:03 am
content: Quote from: RoGeorge on May 31, 2023, 06:42:27 amRighty-o.One problem is that most (all?) things can be described in more than one way. Consider optics and Snell's Law, versus Fermat's Principle of Least Time: the former can be derived from the latter, making them equivalent. The two have very different 'explanations', too – even when they are mathematically equivalent. Ouch.Second problem is that we cannot always even tell whether our mathematical description is correct, or only approximately correct to within some arbitrary decision within the region we can measure. An example of this is how Newtonian mechanics are indistinguishable from relativistic mechanics for small enough energies (masses and velocities).Just like in mathematics, you always have some axioms that cannot be derived or proven in physics too. Physics is aboutmodelingor describing reality, notdefiningit. (Thus, "physical law" = description or model that produces reproducible results matching real world experiments, not a dictat or requirement.)_ _ _ _ _Of course, when we consider say usable oscillators, the problem is not a show-stopper. We just need to outline what an "usable oscillator" is, and then analyse and group them so that we find their commonalities. The simplest set I can find is the division into discrete states or infinitely differentiable amplitude ones, with most "real" oscillators a combination of the two; and this is what my answers above tried to show.Unfortunately, there are many valid answers (groupings and derived commonalities/requirements). Fortunately, it does notmatter, because we can go back to the outline or definition of "usable oscillator", vary the definition or use case a bit, and pick the answer that yields the most useful properties.Indeed, it actually is not unfortunate at all, because the set of different valid answers covers a larger set than any single answer alone; it just depends on the context and viewpoint which one happens to be most useful with respect to a given situation/problem/case.If you think that is cheating or not true, do remember that even your own senses are approximations, inferences, and extrapolations. We don't normally use infinite precision arithmetic in microcontrollers, because it would be a waste of resources. Whenever investigating large molecules or systems of molecules, we don't use quantum mechanics derivedab initiomodels (because it would be too slow!), and use approximate/empirical ("descriptive") potential models instead. We don't use relativistic mechanics for satellite orbits, because Newtonian mechanics gives the same results with much less effort, and the noise (interaction with solar wind, upper atmosphere, and magnetosphere, among other things) causes larger unpredictable errors than the difference between the two.Perfect is the enemy of good: approximations and even guesses lets us advance, when requiring exact correctness would stall us.In a very real way, even the 'irreducible basic components needed' kind of 'why' is almost impossible to answer, at least at this point. Even if we had the language to describe it, we don't have the context in which it would make sense, be understandable to us humans. It is annoying, but we are very imperfect beings. We have to settle for the best approximation we have for it, and make do.Remember, modern physics is barely a century old.Anyone claiming "most of physics has been discovered already", is just repeating a variant of the "640k of RAM is enough for everyone".Or heck, what doIknow; I could be utterly wrong here.Just trying to help you find ausefulpoint of view and understanding.

author: TimFox
author_rank: Super Contributor
timestamp: May 31, 2023, 01:38:56 pm
content: Quote from: RoGeorge on May 30, 2023, 09:02:06 pmEven though most occurrences have a cause, they do not need to have a reason.

author: jwet
author_rank: Frequent Contributor
timestamp: June 02, 2023, 04:49:28 pm
content: Nominal- There is a philosophy that teaches that there is only one ultimate truth but an infinite number of ways to observe it. The older I get, the more I believe this I think, though I'm no closer to knowing the ultimate truth. If this idea intrigues you, check out an interesting book - "The Surrender Experiment" by Michael Singer- it takes this to a very useful result.One of the funny and useful things about online forums is that you see this at work- everyone brings their own truth to their understanding of the poster's problem.I enjoy this thread- kind of a diversion.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: June 02, 2023, 07:45:50 pm
content: Quote from: jwet on June 02, 2023, 04:49:28 pm.This post also hints at one of the qualities of a good teacher. The very best can identify the student's truth and provide explanations that are likely to be effective from that point of view, and ideally expanding understanding.

author: aneevuser
author_rank: Frequent Contributor
timestamp: June 03, 2023, 12:54:54 pm
content: Quote from: IanB on May 23, 2023, 01:39:00 pmInteresting thread.The quote above is too restrictive though. There are higher order DEs which can be proven to oscillate, though I'm not at all familiar with the methods (and as you note later, coupled first order DEs like Lotka-Volterra can also oscillate - do we count them as "really" second order?) - there is a branch of DE maths called oscillation theory which treats these problems.

author: jonpaul
author_rank: Super Contributor
timestamp: June 03, 2023, 03:10:20 pm
content: Simple answer:Loop gain > 1Works for any osc, mechanical, electric, electronic.Jon

author: SiliconWizard
author_rank: Super Contributor
timestamp: June 04, 2023, 01:53:58 am
content: Everything is an oscillator.

author: The Electrician
author_rank: Frequent Contributor
timestamp: June 04, 2023, 02:20:38 am
content: There was a lady on the Coast to Coast radio show:https://en.wikipedia.org/wiki/Coast_to_Coast_AMthe other night who informed the listeners that everything in the universe has a frequency. There must be a lot of oscillators keeping it all going.

author: AndyBeez
author_rank: Frequent Contributor
timestamp: June 04, 2023, 05:37:07 pm
content: Is white noiseoscillation?

author: TimFox
author_rank: Super Contributor
timestamp: June 04, 2023, 05:44:26 pm
content: No, it is "variation".Inherent in the term "oscillation", starting with the physics of harmonic oscillators and the engineering of feedback oscillators is that the action be periodic.

author: AK6DN
author_rank: Regular Contributor
timestamp: June 04, 2023, 05:54:24 pm
content: Two requirements for an oscillator:1) a feedback loop2) gain greater than unity

author: TimFox
author_rank: Super Contributor
timestamp: June 04, 2023, 06:04:33 pm
content: Quote from: AK6DN on June 04, 2023, 05:54:24 pmThe title of this post is "what's the minimum(physics first)to get an oscillator?" (emphasis supplied)As I keep pointing out, in physics an "oscillator" does not have to produce a sustained output, as does a feedback oscillator in engineering.Even in engineering, there are non-feedback oscillators (such as negative-resistance or relaxation oscillators).

author: metebalci
author_rank: Frequent Contributor
timestamp: June 12, 2023, 06:57:28 pm
content: Quote from: aneevuser on June 03, 2023, 12:54:54 pmLotka-Volterra is second order, isnt it ? Why "really" ? There is a pair of first order equations.I think an oscillation can happen in one dimensional discrete systems but for a continuous one two dimensions are needed (not possible to have two unstable points next to each in one dimension I think?)