Advanced Vibration
Ex. 2
Submit:
Monday, February 28, 2011
1.
Consider the system shown in Figure 1.
(a)
Write the differential equation of motion for the system.
(b)
Determine its poles and mode shapes analytically by using persymmetry. Compare
your result to that obtained by Matlab.
Figure 1
2.
A force
( )
t
t
f
4
sin
=
is applied to the system shown in Figure 2. The initial conditions
are:
( )
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
0
1
0
x
and
( )
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
2
0
0
x
&
.
(a)
What is the steady state amplitude of the system?
(b)
Simulate and plot the dynamic of the system for the time interval
5
0
≤
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 Fall '08
 Ram,Y
 initial conditions, Determine its poles

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