Problems 4: UNIZOR.COM - Physics4Teens - Waves - Mechanical Oscillations
Channel: Zor Shekhtman on UNIZOR Education
Date: 14/11/2021

UNIZOR.COM - Physics through a Looking Glass of Mathematician
Notes to a video lecture on http://www.unizor.com

Problems 4

Problem A

As presented in the lecture "Forced Oscillation 1", the general solution to a differential equation that describes forced oscillation looks like
x(t)=F0·cos(ω·t)/[m(ω0²−ω²)] + D·cos(ω0·t−φ)
where
F0 is an amplitude of a periodic external force;
ω - angular speed of a periodic external force;
m - mass of an object on a spring;
k - elasticity of a spring;
ω0=√(k/m) is an inherent natural angular speed of oscillation of this particular object on this particular spring;
t is time;
D and φ parameters are determined by initial conditions for x(0) and x'(0).

Consider forced oscillations used as an example in that lecture.
Oscillations of a system has its own natural angular speed ω0=2(rad/sec), while a periodic force applied to it has its angular speed ω=5(rad/sec).
Initial displacement and speed are at zero.

Are the forced oscillations periodic?
If yes, what is the period of oscillations?

Solution is presented in the notes to this lecture on UNIZOR.COM.
Follow the links:
"Physics 4 Teens" - "Waves" - "Mechanical Oscillations" - Problems 4"


Problem B

Let's solve a problem that combines free oscillations, viscosity and external periodic force acting on an oscillating object.
Making all the reasonable assumptions, derive the equation of motion of such oscillations.

Solution is presented in the notes to this lecture on UNIZOR.COM.
Follow the links:
"Physics 4 Teens" - "Waves" - "Mechanical Oscillations" - Problems 4"