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Cooperative Problems Week 14: Oscillations
1.
Your task is to design a damped
harmonic oscillator consisting of a mass of
0.050 kg on an ideal spring.
The damping
is supplied by a linear drag force f
d
= –bv,
where v is the oscillator's velocity.
The
oscillator's free oscillations are to behave as
shown in the graph.
(a)
What is the quality factor "Q" of this
oscillator? [Hint: Q is
π
times the number
of cycles for the amplitude to decrease to
1/e times its initial value.]
(b) What are the values of A
0
( > 0),
τ
,
ω′
, and
φ
in the expression for the oscillator's position
as a
function of time t:
x(t) = A
0
e
–t/
τ
cos(
ω′
t +
φ
)? What is the mathematical relationship between Q,
τ
, and
ω′
?
(c)
What are the appropriate values for the spring constant k and drag force constant b? [Hint:
τ
= 2m/b;
for light damping,
ω′
≈
/
km
.]
Displacement
(mm)
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View Full Document(d) Now the oscillator is driven by a sinusoidal applied driving force at angular frequency
ω
.
The
oscillation amplitude as a function of
ω
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 Spring '07
 LECLAIR,A
 Physics, Force, Mass, Simple Harmonic Motion, damped harmonic oscillator

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