1
Phy 3221
Due: February 23, 2011
Homework set # 6
If you expect credit for your homework, then it is best to make it easily readable.
Some of these problems might be of use while preparing for the test in class on Feb. 16.
Problem
1: From the textbook: Prob. 39
Problem
2:
Two masses
m
1
and
m
2
(
note:
m
1
6
=
m
2
) are on a table at either end of
a horizontal spring of unstretched length
L
and spring constant
k
which is lined up along
the
x
axis. Assume that there is no friction. Initially the masses are held in place so that
the spring is stretched. Let
x
1
and
x
2
be the positions of the two masses and assume that
x
2
> x
1
.
At a given moment the forces on the two masses are
F
2
=

(
x
2

x
1

L
)
k
and
F
1
= (
x
2

x
1

L
)
k
=

F
2
.
When the masses are released, they will oscillate at the same frequency.
a. Use
F
=
ma
=
md
2
x/dt
2
and derive a single diﬀerential equation for the combination
x
2

x
1

L
.
b. What is the frequency of the oscillations of the masses?
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 Spring '08
 CHAN
 mechanics, Mass, Simple Harmonic Motion, Work, masses, damped harmonic oscillator

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