PHYSICS 200
PROBLEM SET #9
Due November 11, 2009
Read Serway and Jewett Ch. 15.
1)
Consider a damped, driven harmonic oscillator as discussed in class. Show that the maximum
amplitude of motion occurs when the drive frequency is
()
22
max
0
/2
ωω
γ
=−
where
is the damping coefficient. Show that in the limit of small damping,
ω
max
goes to
0
.
2)
A harmonic oscillator with natural period (i.e., in the absence of dapming)
T
= 0.1 s is placed
in an environment where its motion is damped, with a damping force proportional to its speed.
The amplitude of the oscillation drops to half of its original value in 5.0 s. What is the period of
the oscillator in the new environment?
3)
A uniformly dense book of dimensions 7 cm x 14 cm x 21 cm has a mass of 3 kg. You pick it
up close to one corner with a pair of calipers and let it swing. What is the angular frequency for
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 Fall '08
 JOHNSON
 Chemistry, pH, Mass, Simple Harmonic Motion, ωmax

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