ME 375
HOMEWORK #7
Fall 2010
Out:
October. 15
th
, 2010
Due: October 22
th
, 2010
PROBLEM 1
:
(30%)
(a)
The model of a certain mass-spring-damper system is
10
20
( )
x
cx
x
f t
+
+
=
&&
&
How large must the damping constant
c
be so that the maximum steady-state amplitude of
x
is no greater
than 3, if the input is
( )
11sin
f t
t
ω
=
, for an arbitrary value of
ω
?
(b)
The dynamic equation of a second order system subject to a sinusoidal input can be written as
2
0
2
( )
sin
n
n
x
x
x
f t
f
t
ζω
ω
ω
+
+
=
=
&&
&
The figure below shows the scaled input
0
( )/
f t
f
and the steady state response
( )
x t
.
Find the natural
frequency
n
ω
and the damping ratio
ζ
of the system.
PROBLEM 2
(30%)
Sketch the Bode plots of the following transfer functions using asymptotes.
Show your work clearly.
After
completing the hand sketches, verify your results using MATLAB.
Turn in your sketches and the MATLAB
results on the same scales.
(a)
100
( )
(0.1
1)(0.5
1)
G s
s
s
s
=
+
+
(b)
2
1
( )
3
10
G s
s
s
=
+
+
(c)
2(
5)
( )
(
10)
s
G s
s s
+
=
+

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