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Physics 214, Spring 2009
1
Cornell University
Physics 214 Assignment 2
Concepts:
damped oscillations
traveling waves
driven oscillatons and resonance
wavelength, frequency
damping regimes
power in driven oscillations
Reading:
AG Lecture Notes on Mechanical Waves (from website); Y&F, Vol. 1, Chapter 15
Assignment:
Due in lecture on Tuesday, February 3.
Please turn in this sheet stapled to the top of your work.
Physics Problems:
1.
Free oscillations.
(a) The online lecture notes give expressions for x(t) in the underdamped, overdamped and
critically damped cases, in terms of
and
. Sketch the shape of the solution for x(t) in
each of these cases, on same set of axes. In all cases, assume the initial conditions
x(t=0) = A and v(t=0)=0.
(Feel free to use a spreadsheet/plotting program.)
(b) In the underdamped case
, show that the imaginary part of
- which gives the
frequency of oscillations, has a magnitude
What must
0
A
be so that the oscillation frequency deviates from
0
by (i) 0.1%?
(ii)
1%?
(iii) 10%?
(c) What is special about the critically damped case?
For each of the following systems,
would you like the response to be underdamped, overdamped, or critically damped?
Explain briefly.
(i) Auto suspension system; (ii) door bell; (iii) speaker cone; (iv) pogo
stick; (v) cymbal; (vi) drum head; (vii) spring bathroom scale; (viii) bungee cord + person.
2.
Driven oscillations.
In lecture we derived the following expression for the complex
amplitude of the response of a driven damped oscillator:
(a) Determine expressions for the magnitude
and phase
of

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