MA 107
Modeling And Analysis of Dynamic Systems
W06
Professor TC. Tsao
HW 8 Solution
1. 5.1 and determine stability of the system.
The pole of the transfer function is at 2.
So the system is stable.
2
5.2 and determine stability of the system.
The pole of the transfer function is at 13.
So the system is stable.
9.21
has a peak value of about 20dB.
Therefore the harmonic floor vibration Y must be
less than X/20 dB = 2mm/10 = 0.2 mm.
>>m=500,c=1600,k=5e5;
>> bode([c k],[m c k]);
80
60
40
20
0
20
Magnitude (dB)
10
0
10
1
10
2
10
3
10
4
180
135
90
45
0
Phase (deg)
Bode Diagram
Frequency
(rad/sec)
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Modeling And Analysis of Dynamic Systems
W06
Professor TC. Tsao
4.
9.37
The bandwidth is somewhat larger than the natural frequency (70 rad/sec) because of the
numerator term.
From the Bode plot, we identify the bandwidth (3 dB or 0.707 from the
DC gain) to be about 140 rad/sec.
So the solution above should have calculated one more
term at 40
π
rad/sec.
The gains and phases may also be read from the Bode plot if the plot
gives sufficient resolution.
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 Spring '06
 TSAO
 Decibel, Modeling And Analysis of Dynamic Systems, Professor TC

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