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Systems Dynamics and Controls Exam 2 Material

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Ex)
-
m
"
. 43
EFm
,
mis
↓
Mix
=
,
Empr + b
(m s
,
+
2(mes"
(mis
spring
and
,
for
accounts
->
=
=
=
ba)
+
K
,
,
b
=
mi
(22-21)
Es ,
+
=
,
sie
,
Fb2 -As ,
bina
+
Fb
(b ,
=
s
+
+
(b
,
+
↓
.
Foc
4
,
be
i
o
closer
,
bi
=
,
kx
+
,
+
K2y
+
x
big -
,
and
22
unknowns
k)xc()
(k + (2)] Xy(s)
4)/m2st
Its
Kik2
+
(k + kel
+
(D)
-
,
ignore weight
M2
a
is
Fbc
+
FS2
!
>
-
my
H
(12 x1)
,
2 FOMs
222
-
Fr2:ki in a
my
(b, + b) s
bis
Position for
I
N
biS+ ()X
+
+
,
+
FS
=
Fb ,
but Rix
+
IDOF
-
Es
mini
=
Equilibrium
Static
.
"eB4bn
,
QUARTER CARMODEL
,
-xx2
me
↑ EFm
x
.
bz)s
+
(b
=
(
+
,
S +
k)X (b)
,
kz) X (b)
,
=
(b
+
,
+
s+
(b
,
k)(b
kz)Y(3)
+
s
,
S
(b , s + k)(b
k)X(S)
+
>
) +
kz) Y())
Im
&
xWdz
(bis k)(bes + ke)
x
+
X
"(mis
Wd ,
>
L
+
b, s +
(n) (M
-
32
+
(b, + bu)s
+
k
+
K2)
(bis the -
-
X-Wd ,
X-Wdz
z
2 ult)
:
A cos(wct)
,
+
Azsin(Wdit)
+
Bicos(weet) + Besin/wdzt)
X
·
Possibilities
i
-
-
S
2
of eigs
conjugate pairs
complex
4 real
eigs
a
W
C
todo to to
S
I
-
E
V
RH)
:
Ge
+
C (etoot
+
+
Ge-1007
Re
-
for
y
what
is
C
--
I
I
for
7
of
replated
what
,
SS
tr
U
I
- 2 sets
six
S
!
=
value
does
going
to
look
be
like
?
:-k2"
ress
I
-
reals
be
:
Y
Stain
*
*
N
I real
-
2
:
complex
&
*
+
n
x
I
,
(t)
- & I w,
S , Wa
*
*
=
GeBiWn'cos (wd
,
+
+
(2) +
Are
I
sten response of
-
2
is
-
Example-gain
and
phase
-
ECP . St
8)
-
>
-
tan
:
Poles
Zeros
Elju)
:
:
IpH)
factb/
(E)
of
order
for
systems
VU
=
Asincut
d
-
awa)
Fan
roots of denominator
rool
higher
for
numerator
or
:
Use t
O
Faced)" (2)2
+
-
phase
egenvalues
complex pairs of
eigenvalues
-↓
=
(ebewuztcos(wdft
M
p
W
Gain
pairs
-
W
wda
Wd
C complex
:
+
(H)
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