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Physics 340
Fall 2003
Exam 1
25 points each
1.
A simple harmonic oscillator has period T = 1 second. Its displacement is given by
sin
(
)
x
at
wf
=+
If the oscillation started at t = 0 from initial position x
0
= 0.5 m with initial velocity
v
0
=
π
m/s, find
φ
and a.
2.
A particle of mass m slides freely on a frictionless parabolic track under the influence of
gravity. Use g =10m/s
2
. The shape of the track is
2
(
)
0.
1
meters
y
xx
=
a.
What is the position of stable equilibrium?
b.
The mass is displaced a small distance from equilibrium and let go. Show that the
motion is simple harmonic oscillation and find the angular frequency.
c.
Say the track actually has frictional forces given by
2
Newtons
3
0
x
y
m dx
F
dt
F
=
=
In this case what is the angular frequency of the damped motion?
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 Fall '08
 Clarke
 Physics, Heat

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