1
n
n
R
(
s
)
−
Response
(
d
B
)
University
of Wollongong
MECH321 Autumn
2016 -
Tutorial
7
Solution
1. Calculate the
DC gains
(in dB) of the three
systems described
by the following
transfer functions (2 Marks),
6
ω
2
G
1
(
s
)
=
,
G
2
(
s
)
=
s
2
+
2
ζ
ω
n
s
+
w
2
s
2
+
7
s
+
22
(
s
+
3)(
s
2
+
2
s
+
3)
,
G
3
(
s
)
=
s
(
s
+
1)
(
s
2
+
9)(
s
2
+
2
s
+
4)
Answer:
G
1
(
s
→
0)
=
6
⇒
15
.
56
dB
,
G
2
(
s
→
0)
=
2
.
44
⇒
7
.
76
dB
,
G
3
(
s
→
0)
=
0
⇒
−∞
2. For a
suspected second
order dynamic system the transfer function cannot
b
e
determined mathematically. Instead the magnitude plot of the transfer function
G
(
s
)
=
C
(
s
)
is
experimentally measured
and is given below,
M
ag
n
it
ud
e
plo
t
of
t
h
e
second
o
r
d
e
r
s
y
s
t
e
m
10
5
0
−
5
−
10
−
15
−
20
−
25
−
30
−
35
−
40
−
45
−
50
−
55
60
10
−
1
10
0
10
1
10
2
F
r
e
q
u
e
n
c
y
(r
a
d
/
s
)
An A4 copy of this graph and an
expanded
graph showing the peak detail are
available
on
e-Learning
if needed.
(a)
Determine
the damping ratio
ζ
, the natural
frequency
ω
n
and
th
e
bandwidth
ω
b
of the
system.
(1
Mark)

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