PHYS 3202 Classical Mechanics II  Homework #9
Due at 12:05pm, Friday April 15, 2011 in the class
Please show intermediate steps of your calculations. If necessary, you
may draw diagram(s).
Problem 1
(10 points): Two identical massless springs with spring constant
κ
each and two particles of mass
m
each are connected in an array. Spring 1 connects
a ﬁxed wall and particle 1, spring 2 connects particle 1 and particle 2. Particle 1 is
in the middle. Let the displacement of the
j
th particle from its equilibrium point
be
q
j
. Find the characteristic frequencies of the system. Omit gravity. If
q
1
(0) = 0
,
q
2
(0) =
±,
˙
q
1
(0) = ˙
q
2
(0) = 0
,
ﬁnd
q
1
(
t
) and
q
2
(
t
) as functions of the time
t
.
Problem 2
(10 points):
n
identical springs, with spring constant
κ
each, and
n
particles of mass
m
each are connected in a linear array: spring 1 connects a ﬁxed
wall and particle 1, spring
j
connects particle
j

1 and particle
j
, where
j
= 2
,
···
,n
.
The
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 Spring '11
 Tan
 mechanics, Energy, Kinetic Energy, Mass, Work, identical massless springs, characteristic frequencies

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