ME 375 – Fall 2010
Homework No. 5
Due: Friday, October 1
Problem No. 1 (40%)
A force
f t
( )
=
f
0
u t
( )
is applied to block A of the twoDOF system shown above.
Assume all surfaces to be smooth and that the springs are unstretched when
x
1
=
x
2
=
0
.
For this system:
a)
Derive the EOMs in terms of the coordinates
x
1
and
x
2
.
b)
Develop the transfer function
G s
( )
=
X
2
s
( )
/
U s
( )
corresponding to an output of
x
2
t
( )
and an input of
u t
( )
.
c)
Determine the four poles
p
1
,
p
2
,
p
3
,
p
4
(
)
of the transfer function in b). Plot these
poles in the complex plane. Use
m
=
1
kg
and
k
=
100
N
/
meter
.
d)
Based on the poles found in c) above, classify the stability of the system (unstable,
stable or marginally stable).
e)
Suppose that we are interested in the forced response of
x
2
t
( )
for an input of
u t
( )
=
!
t
( )
=
unit impulse function
. With this input, we know that the partial
fraction expansion of the response
x
2
t
( )
can be written as:
x
2
t
( )
=
A
1
e
p
1
t
+
A
2
e
p
2
t
+
A
3
e
p
3
t
+
A
4
e
p
4
t
. Based on the poles found in c), provide a
qualitative description of these components of this response. Address the following
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 Fall '10
 Meckle
 1 kg, 20%, 3k, 40%, 2%

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