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Physics 1C, Summer 2011 (Session 1)
Midterm 1 (50+5 points) Solutions
Problem 1 (4+4+6 = 14 points)
A particle is undergoing simple harmonic motion. Its velocity is given by the equation
v(t) = (230 m/s)*sin[(1000s
1
)*t]. Give the answers to the following questions in SI
units:
a. What is the amplitude of the particle's motion?
b. What is the period of the oscillatory motion?
c. What is the first time t after t = 0 seconds that the particle will reach its equilibrium
position?
Solution
a. The maximum speed is 230 m/s =
ω
A, where A is the amplitude and
ω
= (1000s
1
) can
be read off from the problem statement. This gives A = 0.23 meters.
b. The period T = (2
π
)/
ω
= 6.3 ms.
c. This is the value of t for which (1000s
1
)*t = (
π
/2) radians: t = 1.57 ms.
Problem 2 (4+4 = 8 points)
Suppose you would like to create a pendulum with a 10 kg bob such that the period is
exactly one second.
a. What length of string should you use to create your pendulum?
b. What length of string should you use if instead you use a 20 kg bob?
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 Spring '07
 Smith
 Simple Harmonic Motion

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