University of Michigan
Physics 340, Fall 2003
5 Sept. 2003
Assignment 1: The Harmonic Oscillator, Complex Representations, Superposition
Required
reading: French, Chap. 1
Chap. 2 through p 26
Chap. 3 through p 62
We start with a version of the basic physics problem for the harmonic oscillator:
1.
A block of mass m=0.5 kg is free to oscillate at the end of a spring. At time t = 0, the block is
launched from its rest position at x = 0, by a hammer strike which imposes an instantaneous
velocity v
0
= 40 cm/s. The block then executes simple harmonic motion with a maximum
excursion of A = 10 cm.
a)
Find the oscillation frequency, the period, and the spring constant. (Hint: Write an
expression for the position of the block as a function of time. Differentiate to find the
velocity. Solve for the initial conditions.)
b)
What is the velocity at t =
π
/4 s? Explain.
c)
Plot the kinetic and potential energy of the block vs. time. (Recall that the potential
energy of a linear spring is given by
2
1
2
U
kx
=
.) What is the total energy vs. time?
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 Fall '08
 Clarke
 Physics, Energy, Kinetic Energy, Simple Harmonic Motion, Heat, initial conditions

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