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ME 375
HOMEWORK #8
Spring 2010
Out:
March. 10
th
, 2010
Due: March 17
th
, 2010
PROBLEM 1
:
(30%)
(a)
Sketch the complex plane and shade the region for system poles locations corresponding to a
damping
ratio greater than 0.75
(b)
Sketch the complex plane and shade the region for system poles locations corresponding to a
2%
settling time less than 0.5 seconds
(c)
Sketch the complex plane and shade the region for system poles locations corresponding,
simultaneously, to a
damping ratio greater than 0.75 and a 2% settling time less than 0.5 seconds
(d)
Sketch the possible pole locations for a 2
nd
order system with a natural frequency of 20 rads/second and
positive damping ratio.
Directly indicate the pole locations for damping ratios of 0, 0.5, 0.707, 1 and 2.
PROBLEM 2
(30%)
Sketch the Bode magnitude and phase diagrams of the following transfer functions:
(a)
3
()
42
Gs
s
=
+
(b)
80(
1)
(
5)(
20)
s
ss
+
=
++
Label the break frequencies.
Compare your plots with those generated by MATLAB.
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 Fall '10
 Meckle

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