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DATE:
October 23, 2011
DUE:
October 28, 2011
ENG102, Solution to homework set #5.
x
m
1
m
2
v
2
x=0
k
Look at the figure above. We consider a harmonic oscillator consisting of a spring with
spring constant
k
, connected to a wall at one end and a mass
m
1
at the other. The mass can
move along the
x
axis as indicated. The coordinate of the mass is such that
x
= 0
when the
spring is without tension. At time
t
= 0
the mass is at rest at
x
= 0
. At this time (
t
= 0
)
another mass
m
2
≤
m
1
hits
m
1
with velocity
v
2
. The quantities listed here are considered
known, as is the friction coefficient
α
mentioned below.
Use the results from HW4.
1.
We assume that there is a friction force between
m
1
and the horizontal surface, such that
the force on
m
1
is
f
f
=

α
˙
x
, where
0
≤
α <
2
r
k
(
m
1
+
m
2
)
. We further assume
that the collision between
m
1
and
m
2
is instantaneous and inelastic such that the two
masses move as one after the collision.
a. Write the equation of motion for the united object after the collision.
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 Fall '08
 Eke

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