MEM 351: Laboratory 1
Mark Ilg, Ph.D.
Department of Mechanical Engineering and Mechanics
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Dynamic Systems: Complex Notation - Laboratory I | MEM 351, Study notes of Mechanical Engineering
Lecture 2 Material Type: Notes; Professor: Ilg; Class: Dynamic Systems Laboratory I; Subject: Mechanical Engr & Mechanics; University: Drexel University; Term: Spring 2011;
Typology: Study notes
2010/2011
1 / 10
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MEM 351: Laboratory 1^ Mark Ilg, Ph.D.Department of Mechanical Engineering and Mechanics
(^500) -50 -100 Magnitude (dB) -150 -200 -1^10
011010
231010
(^410)
-90 -135 Phase (deg) -
Bode Diagram Frequency^ (rad/sec)
Frequency Response Review:Continued^ ^ Laplace Transform^ ^ Fourier Transform:
( )^
st ( ) 0
X^ s^
x t e^
dt^ s
j σ ω
∞^ −
−
=^
=^ +
∫ ( ) ( )
j^ t
X^
x t e^
ω dt
ω
∞
− =^ ∫ −∞
Bode Plots
(^ )
(^ )
(^ )
10
10 10 20 log
vs.^ log vs.^ log
G G
M
ω
φ
ω
-1^10
(^0 )
(^1 )
(^210)
-5 -10 -15 -20 -25 -30 -35 -40 -
Bode Plot
Magnitude Response -1^10
(^0 )
(^1 )
(^210)
(^0) -10 -20 -30 -40 -50 -60 -70 Phase Response -80 -
ω
( )^
G s^
=^ s +
Modeling RC Network
∧∧∧
⊥^ (
+^
−^
−
( ) v t^ i
( ) v to
R^ C ( ) i t
( )^
( )^
( )^
V^ s^ o i
G s^
V^ s^
RCs
=^
=^
Frequency Response
R s^ (^ )
G s^^ (^ )
C s (^ )
(^ )^
(^ )^
(^ ) 2 2
1 sin^
cos cos tan r t^ A
t^
B^
t^ B A^ B^
t^
A ω
ω −ω =^
+^ ^
=^ +
−^
^
^
( )^ As^ B^2 R s^
ω + = s ω+
^ What is the frequency response?
(^ )^
c t^ =
System Identification
Unknown
Unknown
Known
Measure
Unknown
( )^
v