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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 5.
Please turn in this sheet stapled to the top of your work.
Physics Problems:
1.
Damped oscillators.
In our consideration of damped and driven oscillations with a
damping force F = bv, we've focused so far on the case of light damping, This
corresponds to
ω
0
τ
/2 >>1 where
ω
0
2
= k/m and
τ
= 2m/b,
so that there are many free
oscillations in one decay time.
Let's explore the more general case.
(a)
Free oscillations.
Using the complex representation z(t) = Ae
α
t
in the equation of
motion, obtain an equation for
α
.
Determine the solutions to this equation for (i)
ω
0
τ
>1
(underdamped),
(ii)
ω
0
τ
=1 (critically damped) and (iii)
ω
0
τ
<1 (overdamped), where
ω
0
2
=
k/m and
τ
=2m/b.
In each case, write down the solution for x(t) implied by the solutions
for
α
, in terms of
ω
0
and
τ
.
(Note: there may be more than one solution for a given
ω
0
and
τ
, so x(t) will in general be a sum of the solutions.
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 Spring '08
 THORNE
 Power, Cornell University

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