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2Ns(37+/

I 3Ns/m

↑ 5kgm GN/m -um- (^) - -M!ss!s f(t) ust I

He x2ft)

• (^) -

4x E 4xj 4x üz

E!se (^) Me N 24xz

L E 4x !

24x ↓ as!

2!

• My

"

bxj

L

5x

() 4x +^ 4x + (^) 8x - 4x2 - 2x = 0

2. (^) 5xz + (^) 3x2 + (^) 4xz -^ 4x^ - b!z =^ F
3. (^) 5xj +^ 5x +^ 5x3 - 2x! - 3x = 0

O G^ C t M

K M A! ~ y e D Tr (^) N! = 4 3-^ Jr^ =^ 2l!gm2 D!^ =^1 N-m-strod Ta

N2= 12

ya (^64) Ne ad Nu= 16 Toksm-m-! Dr = 2N!med D! =^32 Nestod

• K3 I Tea)--m-

Dea Keq Jege Jr^ .

+ 5 +^

53/3Nat

Dea =^

D

. D2 + Da! Keq = K3/4r Teg^ = T. Jea Özft)^

Deg 02() (^) + KegPert)

= Teght)

201) +^ 1302(^ +^ 402(t)^ =^

3TH) 02(s)(205+^135 +^ 4)^ =^3

• b) se

52() +^ 5x(^ +^ )^ +28x()^ =^ HH) X/s)(552+ (^55) + 28) = F(s)

X/5)

Ersu

= (^55) +28 5.

1

• y (^5) YGS)

H!s Des!gn K^ , and^ a^ so^ that^ the closed-kop transfer funct!on^ y!elds I^ second^ ts and 5 % OS! t!st = "tt"s "st"kapol

Ts =^

(^1) = 1 - (^) Sun =^4 sun

• In (^10). 05/

=>

= 0.^69

• • Wh =^

#In(0. 05

Pc(s) =^33 +^1352 +^ (k)^

• (^) 36)s + k^ - a

Pals) = (^) (s2 + (^) 23wns + (^) wn)(s +^ er

= s+(8+ 2252 + 133

. 64 +^

8e)5 + (^33). 64e

Pcs) = pass)

1. 53 = 53

2. (^1352) = (8+els2^ - e^ =^ 5 3)) (36 +^ k)s = (^) (33. 64 + 82) k!^ =^37.^64
3. (^) Kr (^). a = (^33). 64e - a=^4.^468

K! =^37. 64 - a^ =^4.^468

6 x = f(xru) x y =^ g(xu)

F"

Y

!

• (^) = -s"te

sat

=

• !s^ the^ equ!l!br!um (^) po!nt then^ = (^) fer) =^0 = Ese^ :

Let us (^) assume (^) we (^) measure O y = g(x -^ v) = (^) x

=

20 D (^) = /ga