X o d ~ 9 h m s 3 I-zGszI

q = J-7' 4 (lumped)

4 EdIer fcruuard diff scheme

r Shift - f ( f )~( t l some

If t c -a ) '4 (4-43

-rt -3t - t .t I t e I t - e + \ \ e - C

i -C) u (t)

Y CS) 4rqnsfec function -+ Gk) = Q Cs)

K; = \ i ~ (s- 7;) XCS) 9 Residue %orem

5-35;

X T r m s k c $unctions are rc\lled impdne

n --I - &.IT 0-7 y ?+ La-

-('irS+ ccdctilng She inner \ o q :

- d c, 0-- - "in - R L i i + LA - + ec d-4

I + cs (L, s + a,) 4

4 CJ) -m

4

I-', r, 8, - wz N, - rt = - - = - - - To, t GI @ r N2 f'2

cid fie lect?ng 9

-to m a k e

h = h-h,

@ equilibrium

Sflstim O d e r :

4* o r d e r

Pd order

exam 14 P 6'c'' V ; S ~ ~ S -frict;on meff i i lent

R d ; + - i I d+ c

t Rd; , , r = d e dl c b4

+ $(4) = A s h (wt)

~ i m (I- s r n ~ w , , ~ ) -t "Cant ' d 9c (+I = -

a w n wn

1

o first srdw ( free re-s o , ; m ~ ~ ~ s ~ , d e ~

r w = 1. (I - h") 2

bounded

a It)

Def inieions f

Q r o o t

Ch~rr\rtei ls t ic Equa-I-ioion: b ( 5 )

3, #P, .P , - - - p,

fins\ uQ\*e Theorem :

s t e ? i ~ p d k

rsmp i n pu-t

pcusbofic

0 Type s JSem 8 s ( s L + S -e \b)

C- &m 5 \ . -

Qss 5-3 o s(s2ist16) + YCstl) se

f (t' st

n o n - u o ; t - k e d k c k sy+Qfns ; he k- 3alh 0 $ t h e The 4-nble s??'ies +Q

step response :

3-x - d s ~ +, I ~ Q x . */. ouwshook \ = x 100 gss

J C S ) = a,= For acs]

""i2~~+""1

-+ find r~ such *a+

o kooks c\os& to t Trn QGS dom;nbter the r s p o n r e .

Can u ~ g ~ j e +msient p & ~ r n a o c e t o r r n u l ~ l ( A ( , k S , m ~ ~ * / o omihoot )

0

a s o r - otf ua 4-0 c n ~ . l e c t

- - - x u -

BC))= s 2 + 2 s + 4 = Q