OpenLLM-France/wikimedia huggingface dataset:
# Engineering Acoustics/Solution Methods for Electro-Mechanical Analogies

After drawing the electro-mechanical analogy of a mechanical system, it is always safe to check the circuit. There are two methods to accomplish this:

## Review of Circuit Solving Methods

Kirchkoff's Voltage law
"The sum of the potential drops around a loop must equal zero."
$v_{1}+v_{2}+v_{3}+v_{4}=0\displaystyle$
Kirchkoff's Current Law
"The Sum of the currents at a node (junction of more than two elements) must be zero"
$-i_{1}+i_{2}+i_{3}-i_{4}=0\displaystyle$
Hints for solving circuits:
Remember that certain elements can be combined to simplify the circuit (the combination of like elements in series and parallel)
If solving a circuit that involves steady-state sources, use impedances. Any circuit can eventually be combined into a single impedance using the following identities:
Impedances in series: $Z_{\mathrm {eq} }=Z_{1}+Z_{2}+\,\cdots \,+Z_{n}.$
Impedances in parallel: ${\frac {1}{Z_{\mathrm {eq} }}}={\frac {1}{Z_{1}}}+{\frac {1}{Z_{2}}}+\,\cdots \,+{\frac {1}{Z_{n}}}.$

## Dot Method: (Valid only for planar network)

This method helps obtain the dual analog (one analog is the dual of the other). The steps for the dot product are as follows:
Example:
The parallel RLC Circuit above is equivalent to a series RLC driven by an ideal current source

## Low-Frequency Limits

This method looks at the behavior of the system for very large or very small values of the parameters and compares them with the expected behavior of the mechanical system. For instance, you can compare the mobility circuit behavior of a near-infinite inductance with the mechanical system behavior of a near-infinite stiffness spring.
| | Very High Value | Very Low Value |
| Capacitor | Short Circuit | Open Circuit |
| Inductor | Open Circuit | Closed Circuit |
| Resistor | Open Circuit | Short Circuit |

# Additional Resources for solving linear circuits

Thomas & Rosa, "The Analysis and Design of Linear Circuits", Wiley, 2001
Hayt, Kemmerly & Durbin, "Engineering Circuit Analysis", 6th ed., McGraw Hill, 2002
Back to Main page
# Power calculations

When calculating the power dissipation of resistive components, use any one of the three power equations to derive and answer from values of voltage, current, and/or resistance pertaining to each component:
Fhsst electricity86.png
This is easily managed by adding another row to our familiar table of voltages, currents, and resistances:
Fhsst electricity87.png
Power for any particular table column can be found by the appropriate Ohm's Law equation (appropriate based on what figures are present for E, I, and R in that column).
An interesting rule for total power versus individual power is that it is additive for any configuration of circuit: series, parallel, series/parallel, or otherwise. Power is a measure of rate of work, and since power dissipated must equal the total power applied by the source(s) (as per the Law of Conservation of Energy in physics), circuit configuration has no effect on the mathematics.
# Resistors

Because the relationship between voltage, current, and resistance in any circuit is so regular, we can reliably control any variable in a circuit simply by controlling the other two. Perhaps the easiest variable in any circuit to control is its resistance. This can be done by changing the material, size, and shape of its conductive components (remember how the thin metal filament of a lamp created more electrical resistance than a thick wire?).
Special components called resistors are made for the express purpose of creating a precise quantity of resistance for insertion into a circuit. They are typically constructed of metal wire or carbon, and engineered to maintain a stable resistance value over a wide range of environmental conditions. Unlike lamps, they do not produce light, but they do produce heat as electric power is dissipated by them in a working circuit. Typically, though, the purpose of a resistor is not to produce usable heat, but simply to provide a precise quantity of electrical resistance.
The most common schematic symbol for a resistor is a zigzag line:
Resistor values in ohms are usually shown as an adjacent number, and if several resistors are present in a circuit, they will be labeled with a unique identifier number such as $R_{1}$, $R_{2}$, $R_{3}$, etc. As you can see, resistor symbols can be shown either horizontally or vertically:
In keeping more with their physical appearance, an alternative schematic symbol for a resistor looks like a small, rectangular box:
Resistors can also be shown to have varying rather than fixed resistances. This might be for the purpose of describing an actual physical device designed for the purpose of providing an adjustable resistance, or it could be to show some component that just happens to have an unstable resistance:
In fact, any time you see a component symbol drawn with a diagonal arrow through it, that component has a variable rather than a fixed value. This symbol "modifier" (the diagonal arrow) is standard electronic symbol convention.
Because resistors dissipate heat energy as the electric currents through them overcome the "friction" of their resistance, resistors are also rated in terms of how much heat energy they can dissipate without overheating and sustaining damage. Naturally, this power rating is specified in the physical unit of "watts." Most resistors found in small electronic devices such as portable radios are rated at 1/4 (0.25) watt or less. The power rating of any resistor is roughly proportional to its physical size. Also note how resistances (in ohms) have nothing to do with size!
# Polarity of voltage drops

We can trace the direction that electrons will flow in the same circuit by starting at the negative (-) terminal and following through to the positive (+) terminal of the battery, the only source of voltage in the circuit. From this we can see that the electrons are moving counter-clockwise, from point 6 to 5 to 4 to 3 to 2 to 1 and back to 6 again.
As the current encounters the 5 $\Omega$ resistance, voltage is dropped across the resistor's ends. The signs of this voltage drop is negative (-) at point 4 with respect to positive (+) at point 3. We can mark the polarity of the resistor's voltage drop with these negative and positive symbols, in accordance with the direction of current (whichever end of the resistor the current is entering is negative with respect to the end of the resistor it is exiting:
Fhsst electricity00052.png
We could make our table of voltages a little more complete by marking the polarity of the voltage for each pair of points in this circuit:
Between points 1 (+) and 4 (-) = 10 volts
Between points 2 (+) and 4 (-) = 10 volts
Between points 3 (+) and 4 (-) = 10 volts
Between points 1 (+) and 5 (-) = 10 volts
Between points 2 (+) and 5 (-) = 10 volts
Between points 3 (+) and 5 (-) = 10 volts
Between points 1 (+) and 6 (-) = 10 volts
Between points 2 (+) and 6 (-) = 10 volts
Between points 3 (+) and 6 (-) = 10 volts
While it might seem a little silly to document polarity of voltage drop in this circuit, it is an important concept to master. It will be critically important in the analysis of more complex circuits involving multiple resistors and/or batteries.
It should be understood that polarity has nothing to do with Ohm's Law: there will never be negative voltages, currents, or resistance entered into any Ohm's Law equations! There are other mathematical principles of electricity that do take polarity into account through the use of signs (+ or -), but not Ohm's Law.
# Correct use of Ohm's Law

One of the most common mistakes made by beginning electronics students in their application of Ohm's Laws is mixing the contexts of voltage, current, and resistance. In other words, a student might mistakenly use a value for I through one resistor and the value for E across a set of interconnected resistors, thinking that they'll arrive at the resistance of that one resistor. Not so! Remember this important rule: The variables used in Ohm's Law equations must be common to the same two points in the circuit under consideration. I cannot overemphasize this rule. This is especially important in series-parallel combination circuits where nearby components may have different values for both voltage drop and current.
When using Ohm's Law to calculate a variable pertaining to a single component, be sure the voltage you're referencing is solely across that single component and the current you're referencing is solely through that single component and the resistance you're referencing is solely for that single component. Likewise, when calculating a variable pertaining to a set of components in a circuit, be sure that the voltage, current, and resistance values are specific to that complete set of components only! A good way to remember this is to pay close attention to the two points terminating the component or set of components being analyzed, making sure that the voltage in question is across those two points, that the current in question is the electron flow from one of those points all the way to the other point, that the resistance in question is the equivalent of a single resistor between those two points, and that the power in question is the total power dissipated by all components between those two points.
The "table" method presented for both series and parallel circuits in this chapter is a good way to keep the context of Ohm's Law correct for any kind of circuit configuration. In a table like the one shown below, you are only allowed to apply an Ohm's Law equation for the values of a single vertical column at a time:
Fhsst electricity88.png
Deriving values horizontally across columns is allowable as per the principles of series and parallel circuits:
Fhsst electricity89.png
Fhsst electricity90.png
Not only does the "table" method simplify the management of all relevant quantities, it also facilitates cross-checking of answers by making it easy to solve for the original unknown variables through other methods, or by working backwards to solve for the initially given values from your solutions. For example, if you have just solved for all unknown voltages, currents, and resistances in a circuit, you can check your work by adding a row at the bottom for power calculations on each resistor, seeing whether or not all the individual power values add up to the total power. If not, then you must have made a mistake somewhere! While this technique of "cross-checking" your work is nothing new, using the table to arrange all the data for the cross-check(s) results in a minimum of confusion.
# English-Hanzi/Line

A line is a long thin mark that links between two points.
一条 线 是 连接 两个 点 之间 的 细长 标记。
# English-Hanzi/Lisbon

Special:search/Lisbon prefix:English-Hanzi/
Lisbon is the capital of Portugal. Its population is 2.8 million.
Lisbon 是 Portugal 的 首都。它的 人口 是 280万。
# English-Hanzi/Level

A level is the particular height of something.
水平 是 某事物 的 特定 高度。
# English-Hanzi/Libya

Libya is a country in the north of Africa. Its population is 6.3 million.
Libya 是 一个 在 非洲 北部 的 国家。它 的 人口 是 630万。
# English-Hanzi/Life

Life is the state of being alive.
生命是活着的状态。
# English-Hanzi/Lifestyle

Living style is the style of how we live. It includes diet, exercise, rest, and mentality. It is the main factor of longevity. It decided the length of the life.
生活方式 是 我们 生活 的 风格。它 包括 饮食，运动，休息，和 心态。它 是 长寿 的 主要 因素。它 决定了 生命 的 长短。
# English-Hanzi/Light

Light is an energy, as well as a very small particle called photon. We can see things when there is light.
光 是 一种 能量，也是 一种 称为 光子 的 非常 小 的 粒子。有 光 时 我们 可以 看到 东西。
# English-Hanzi/Lipid

Special:search/lipid prefix:English-Hanzi/
Lipid is the general term for all kinds of fat.
脂质 是 各种 脂肪 的 总称。
# English-Hanzi/Linguist

Linguist is a specialist of language.
语言学家 是 语言 的 专家。
# English-Hanzi/Liquid

Liquid is a substance that is not a solid and not a gas.
液体 是 一种 不是 固体 也 不是 气体 的 物质。
# Flexible Learning

Flexible Learning is a set of educational philosophies and systems, concerned with providing learners with increased choice, convenience, and personalisation to suit the learner. In particular, flexible learning provides learners with choices about where, when, and how learning occurs. Wikipedia Dec 06
This page will assist you in understanding the principles of Flexible Learning by exploring related information, ideas and new practices in formal education. After reading through this information, and taking up opportunities for learning support it is hoped you will be able to apply flexible teaching and learning techniques in your own contexts.

# Learning support and accreditation

Otago Polytechnic offers formal learning and accreditation services with their Designing for Flexible Learning Practice course.

# Content

Flexible Learning is a recent concept with many varying interpretations. No one interpretation is correct, leaving room for many interesting and useful ideas. For this reason

## Aligning with an educational organisation
# Projects
## Weblog

Document your progress in a weblog

## Resource list

Establish and maintain a social bookmarking list with links to information relating to flexible learning

## Develop a resource

Choose an issue or consideration relating to flexible learning, (for example: accessibility, digital divides, practical skills learning, assessment) and create an learning resource that reports on the issue and suggests solutions.

## Develop a plan

In your weblog, create an entry that is the start of a plan for developing learning flexibility in your course or field of study. The plan should refer to intended learning outcomes, the typical learner profile, trends and directions in industry or sector, and benefits to learners and educational organisation.
# Floating Point/Arithmetic Errors
## Arithmetic Errors

When performing floating-point arithmetic, there are a number of possible errors that can occur. Some of these errors are generally small, but some are worth consideration. This is especially true in applications like numerical integration or numerical derivatives, where implementing naive algorithms may lead to accumulation of the errors and completely unreliable results.

## References

* The Perils of Floating Point
# Floating Point/Comparing FP Numbers
## Floating Point Comparisons

It has been said by many people that floating point numbers should never be compared directly to each other for equality, although this is not strictly true. This page will discuss some common techniques and fallacies for comparing floating point numbers for equality and inequality.
# Floating Point

This wikibook discusses the IEEE 754 standard concerning floating-point numbers. Beginning chapters of this book focus on newcomers to the standard, who wish to understand and make use of floating point numbers, especially in a programming project. Later chapters of this book, however, focus more on the details of implementation of the IEEE 754 standard. This way, advanced users who want more details, or users who are working to create a floating-point implementation of their own can find the information they need. This book can be used as an ancillary reference source to support other books in the computer science and engineering fields.
Programming examples found in this book attempt to use pseudocode where possible, to prevent an over-reliance on any particular language or platform. Specific examples may utilize a single computer language or assembly language.
Prerequisites to this book include an understanding of exponents and Algebra, and an understanding of binary number representation.

## Table of Contents
### Section 1: Number Representation

* Introduction
* Scientific Notation
* Fixed-Point Numbers
* Floating-Point Numbers

### Section 2: IEEE 754

* IEEE 754
* Floating Point Formats
* Special Numbers
* Normalization

### Section 3: Floating Point Arithmetic

* Rounding
* Floating Point Arithmetic
* Epsilon
* Arithmetic Errors
* Guard Bits
* Comparing FP Numbers

### Section 4: Floating Point Hardware

* Converting FP and Integers
* Exceptions
* Trap Handlers
* Flags
* Floating Point Hardware
* Soft Implementations

### Section 5: Algorithms

* Arithmetic Algorithms
* Exponents and Square Roots
* Trancendentals

## Further reading

* IEEE 754 references
* Let's Get To The (Floating) Point by Chris Hecker
* What Every Computer Scientist Should Know About Floating-Point Arithmetic by David Goldberg - a good introduction and explanation.
* IEEE 854-1987 History and minutes
* Converter
* Another Converter
* The pitfalls of verifying floating-point computations, by David Monniaux, also printed in ACM Transactions on programming languages and systems (TOPLAS), May 2008: a compendium of non-intuitive behaviours of floating-point on popular architectures, with implications for program verification and testing
# Floating Point/Epsilon
## Granularity

Floating point numbers, because they are comprised of only a certain number of bits, have a granularity. They therefore cannot express an infinite amount of fractional values. This means that there is a "Largest Possible Value", ε, that satisfies the following equation:
    $1.0\oplus \epsilon =1.0$
This value is called the machine epsilon of the floating point system.

## Epsilon (ε)

When a real number is rounded to the nearest floating point number, the machine epsilon forms an upper bound on the relative error. This fact makes the machine epsilon extremely useful in determining the convergence tolerances of many iterative numerical algorithms.

## Determining Epsilon

The machine epsilon can be computed according to the formula:
    $\epsilon ={b \over 2}\cdot b^{-p}$
So, for IEEE 754 single precision we have
    $\epsilon =2^{-24}=5.96046447753906\times 10^{-8}$
and for IEEE 754 double precision we have
    $\epsilon =2^{-53}=1.11022302462516\times 10^{-16}$
When $p$ is not known, but $b$ is known to be 2, the machine epsilon can be found by starting with a trial value of, say, 0.5 and successively dividing the value by 2 until $1.0\oplus \epsilon =1.0$ is true.

## Granularity Effects

An effect of this granularity is that some basic algebraic properties don't strictly hold. For instance, if we have three floating-point values, x, y, and z, we can show that:
    $x+(y+z)\neq (x+y)+z$
When the floating-point numbers are used in iterative calculations, round-off and granularity errors can result in large errors.

## References

* ↑ Machine epsilon in wikipedia
# Fluid Mechanics Applications/B-34: Sudden contraction
## Introduction

The sudden contraction in the area/diameter of a ﬂuid jet after it emerges from a circular aperture in a pressurized reservoir is called as vena contracta.
Coefficient of contraction is the ratio of the cross sectional area of the jet at the vena contracta to the area of the orifice. The typical value may be taken as .64

## Checking the vena contracta

Assumption P$_1$A$_1$v$_1$ be the Pressure , Area and velocity of fluid in the tank,
P$_2$A$_2$v$_2$ be the Pressure , Area and velocity of fluid in the orifice,
P$_3$A$_3$v$_3$ be the Pressure , Area and velocity of fluid at the vena contracta,
The diameter of the vena contracta is nearly equal to .64 times the diameter of the original hole . Assume fluid is incompressible
using continuity equation
Ignoring energy losses due to viscosity,Bernoullis' holds for points along streamlines
P$_1$ +1/2 d v$_{12}$ = P$_2$ +1/2dv$_{22}$ (3)
where d is the(constant) density of fluid and P is the pressure using equation (2) and (3)
Considering momentum in the system, the mass flux =dvA
so, momentum flux = dv$^2$A The net flux bounded by area A$_1$ and A$_2$
F ≈ P$_1$A$_1$ - [P$_1$(A$_1$ - A$_2$)] = (P$_1$ - P$_2$)A$_2$ (6)
equating to equation (5)
v$_2$$^2$= (P$_1$-P$_2$)/d (7)
This is the contradiction with equation (4) based on conservation of energy. Then according to Torricelli this contradiction is resolved in nature by a contraction of fluid to area A$_3$ after it passes through A$_2$ The momentum flux is actually
According to Bernoulli's equation in the limit that P$_3$ << P$_2$ The force that causes this change is now
we estimate vena contracta to be A$_3$= A$_2$/2
http://www.physics.princeton.edu/~mcdonald/examples/vena_contracta.pdf

## References

* ↑ Minor losses in pipes, FM white
* ↑ Vena contracta, Kirk T. Mcdonald, Joseph Henry Laboratories, Princeton, NJ 08544, (February 16, 2005)
* ↑ Minor losses in pipes, FM white
# Fluid Mechanics Applications/A:20 Stability and oscillation of floating bodies
## INDRODUCTION

The aim of present work is to determine the stability and oscillation of a floating bodies which requires the basic knowledge of fluid statics like Archimedes principle of Buoyancy and states of equilibrium of a floating body.The various factors on which the stability and oscillation of a floating body depends will be discussed also to analyse things properly.
The equilibrium of floating or submerged bodies requires that the weight of the body acting through its centre of gravity has to be collinear with an equal buoyant force acting through the centre of buoyancy. A submerged body will be in stable ,unstable or neutral equilibrium if its centre of gravity is below, above or coincident with the centre of buoyancy respectively.
Stability of floating body depends on its metacentric height. Metacentre of a floating body is defined as the point of intersection of the centre line of cross section containing the centre of gravity and centre of buoyancy with the vertical line through new centre of buoyancy due to any smaller angular displacement of the body. The distance of metacentre from centre of gravity along the centre line of cross section is know as Metacentric height. For stable equilibrium of floating bodies,metacenter(M) has to be above the centre of gravity(G). Metacentre coinciding with centre of gravity or lying below refers to the situation of neutral and unstable equilibrium respectively.
A stable floating body subjected to small angular displacement by disturbances, such as waves, undergoes an oscillation of simple harmonic type.The time period of oscillation is inversely proportional to the square root of metacentric height. An increase in metacentric height results in a better stability at the cost of comfort due to a reduction in the time period of rolling.
# Foundations and Assessment of Education/Edition 1/Assessment Table of Contents/Assessment Chapter 2: Question Writing
## Core Contents

14 Rules for Writing Multiple-Choice Questions—Timothy W. Bothell CLICK HERE to leave a Reader Response for this article.
Go to Virginia Standards of Learning (SOL) released tests for 2007: Look through a test related to your intended field. Identify at least one question that assesses knowledge and one question that assesses application. http://www.doe.virginia.gov/VDOE/Assessment/Release2007/index.html CLICK HERE to leave a Reader Response for this article.
* Student Soapbox
* Questions? Refer to How to Use This Book
# Foundations and Assessment of Education/Edition 1/Assessment Table of Contents/Assessment Chapter 4: Grading
## Core Contents

The Case Against the Zero—Douglas B. Reeves CLICK HERE to leave a Reader Response for this article.
Using Rubrics to Promote Thinking and Learning—Heidi Andrade CLICK HERE to leave a Reader Response for this article.
* Student Soapbox
* Questions? Refer to How to Use This Book
# Foundations and Assessment of Education/Edition 1/Assessment Table of Contents/Assessment Chapter 3: Assessment for Learning
## Core Contents

The Best Value in Formative Assessment—Stephen Chappuis and Jan Chappuis CLICK HERE to leave a Reader Response for this article.
Learning to Love Assessment—Carol Ann Tomlinson CLICK HERE to leave a Reader Response for this article.
* Student Soapbox
* Questions? Refer to How to Use This Book