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Vibrations and Waves
James Dove
HW #1;
August 23, 2010
Due Thursday, Sep 2, (4:30 PM)
29 Points
Harmonic Oscillators and Complex Numbers
1. (5 points) A horizontal harmonic oscillator contains a spring with a spring constant
k
= 100
N/m with an block of mass
M
= 5 kg. At
t
= 0, its position is
x
= 30 cm and its velocity is
v
=

0
.
5 m/s.
(a) Express the position of the block as a function of time,
x
(
t
), both in the form of
x
=
A cos
(
ωt
+
φ
) and
x
=
c
1
cos(
ωt
) +
c
2
sin(
ωt
).
(b) What is the amplitude of oscillation?
2. (5 points) A spring is standing upright on a table with its bottom end fastened to the table.
A block is dropped from a height 3.0 cm above the top of the spring. The block sticks to the
top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation
frequency? (Amazingly, you do not need to know the mass of the block!)
3. (5 points) A platform is executing simple harmonic motion in a vertical direction with an ampli
tude of 5 cm and a frequency
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