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ME 375
HOMEWORK # 7
Spring 2009
Out:
March 4, 2009
Due:
March 11, 2009 (at the beginning of class)
PROBLEM 1:
(30%)
Consider the following differential equation of motion relating an input
f(t)
to the corresponding output
x(t)
:
() 2 () 2 ()
()
(0
) 0
)
x
tx
t
f
t
x
x
++=
=
=
±±
±
±
Answer the following questions:
(a)
Calculate the transfer function relating the input Laplace transform
F(s)
to the output Laplace
transform
X(s)
.
(b)
For a unit step input, solve for the steadystate output using the final value theorem.
(c)
Calculate the frequency response function between the input and output.
(d)
For
f
(
t
)
=
1
for
t
>
0, find the steadystate output using the frequency response function.
(e)
For
f
(
t
)
=
sin 0.1
t
+
cos 1.5
t
, find the steadystate output using the frequency response
function.
(f)
For
x
(
t
)
=
sin
t
−
0.1
+
2 in the steady state, find the forcing function.
(g)
Now suppose that you use an imperfect sensor to measure
x(t)
such that
0.1 ( )
( )
( )
yt
xt
+
=
±
where
y(t)
is the measurement of
x(t)
. Calculate the frequency response function between the true
output,
x(t)
, and the sensor output,
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 Spring '10
 Meckle

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