Question

Question S) Compute the initial and final value of the system using the properties and verify the answer with the impulse response: Note for all these functions the ROC is Re(s) >O. S+3 s3+3s2 +2s 10 b) G(s)= 25

Answer 1

| a) Fls] = a) P(S) = 5+3_ $(52 35+2) em i Snital value theorem It f(t) = 14 s F(s) to sto = lt s*$(t+ 3s) sto sx8*(1+3+2/²) in nu; 1 RO It f(t) =0 ہدا e to FCE). z () zo Finally value theorem: to use Hotel Hot SFC 14 S13 sto 8(3435+2) = 2 it f(t) = 8/ - SX tto

Verification by impulse response : Fore st in de rus) On applying partial fractions Fb) = f t test H. A[5435+2)+B[415)+c[645] s(s+1)(5+2) ? solvin AO At B+C =0 3AF2B+c=1 2A=3 34-72610=1 on solving we get | A= 3/2 B2- (= 1/2 FC) = 1 + 2[512] Jon applying inverse laplace transform f(t) = Luct) – zetuce) +eztult). initial value cat too): f(t)= 1-2+=0 [Itf(t) = 0 I too final value (at t=oo): f(t)= -zabatu eta = 2-2(0)+10 =/ it flt) = ²

d) G(s) = 10 5425 10 G(s) = (575;) (5-58) we cannot apply initial and final value theorems to marginally & unstable system. . We cannot apply for als).