ASSIGNMENT 1
Physics 218
Due Feb. 2
Spring 2008
Reading: Pain Ch 14.
1. Consider the following complex solution to a simple harmonic oscillator problem for a pen
dulum,
z
(
t
) = 12 cm exp[
i
(12
π/st
+ 3)] exp[

(0
.
25
/s
)
t
], where cm and
s
are centimeters and
seconds, respectively, and
t
is time.
(a) Based on the equation, is this pendulum damped? Driven? Justify your answer.
(b) Draw
by hand
a graph of
x
(
t
) vs
t
for 0
< t <
5
s
.
(c) Which of the list of variables
r, s, ω, ω
0
,
ˆ
ω, γ, F
0
, α
and
φ
can you extract from the equation
above, and what are their values? Include units.
(d) What is the period of oscillation of the pendulum (in seconds)? Is there any other
characteristic time in the problem?
2. Show that one can ignore gravity when one studies the harmonic
motion of a mass hanging on a spring. To answer the question,
consider a mass
m
hanging on a spring with negligible mass and
spring constant
k
. Let the length of the spring without the mass be
`
0
and the length of the spring with the mass hanging on it at rest be
`
.
Let
y
(
t
) be the displacement of the end of the spring from the
equilibrium position when the mass is oscillating.
m
o
l
l
(a) Draw a free body diagram of the mass, including the spring force and the force of gravity
on the mass.
(b) Utilize this diagram to determine the length of the spring
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 Spring '08
 PETERWITTICH

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