ME 375 – Spring 2011
Topics Covered on Exam No. 2
Steadystate response to harmonic excitation
Y s
( )
=
G s
( )
U s
( )
=
N
1
s
( )
N
2
s
( )
...
N
m
s
( )
D
1
s
( )
D
2
s
( )
...
D
n
s
( )
U s
( )
For
u t
( )
=
sin
ω
t
:
y
ss
t
( )
=
G j
ω
(
)
sin
ω
t
+
∠
G j
ω
(
)
(
)
where
1
G j
ω
(
)
=
Real
2
G j
ω
(
)
{
}
+
Imag
2
G j
ω
(
)
{
}
=
N
1
j
ω
(
)
N
2
j
ω
(
)
...
N
m
j
ω
(
)
D
1
j
ω
(
)
D
2
j
ω
(
)
...
D
n
j
ω
(
)
∠
G j
ω
(
)
=
tan
−
1
Imag G j
ω
(
)
{
}
Real G j
ω
(
)
{
}
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
=
∠
N
1
j
ω
(
)
+
∠
N
2
j
ω
(
)
+
...
+
∠
N
m
j
ω
(
)
− ∠
D
1
j
ω
(
)
− ∠
D
2
j
ω
(
)
−
...
− ∠
D
n
j
ω
(
)
are the amplitude and phase frequency response functions (FRFs), respectively.
Plots of
G j
ω
(
)
dB
and
∠
G j
ω
(
)
vs.
ω
(on a
log
10
ω
axis) are known as the Bode plots
for the steadystate harmonic response. If
N
k
s
( )
and
D
k
s
( )
represent constant, linear
and quadratic factors of the numerator and denominator of
G s
( )
, respectively, the
amplitude Bode plots for these factors can be approximated by the following dB
lines/asymptotes
2
:
•
K
:
constant
20
log
10
K
(
)
straight line for all
ω
[EXACT]
•
s
±
1
:
straightline for all
ω
with
±
20
dB
/
dec
with
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 Fall '10
 Meckle
 Electrical Engineering, Fluid Dynamics

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