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Prelim 2
Math 293
Spring 2007
show work, 5 questions
no calculators, you need not simplify answers
1)
A train moves on a track. The track has joints and other variations which
repeat every 10 meters, and we will assume these to be sinusoidal. We model
the vertical position
y
(
t
) of the freight car using
my
±±
+
ky
=
f
0
sin(
ωt
)
.
The mass
m
will depend on whether the car is loaded or empty.
a)
(5 points)
What should we take for the value of
ω
, if the train runs at 20
meters per second?
b)
(5 points)
The empty freight car has a mass of 20 000 kg. When loaded
with an additional 80 000 kg load, the springs depress an additional
.
02 meter.
What values should we use for
m
and
k
in the equation of the loaded car?
(Remember weight=
mg
,
g
= 9
.
8.)
c)
(5 points)
The forced response which is observed under these conditions
is
y
=
.
003 sin(
ωt
), i.e., the loaded car vibrates vertically with an amplitude
of 3 millimeters. Find an expression for
f
0
in terms of the other parameters.
(You don’t have to simplify it, but if you want to check it, it ought to be
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 Spring '07
 TERRELL,R
 Math

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