Question

Problem#3 (16 points) Consider a system that has R(S) as the input and Y (S) as the output. The transfer function is given by: Y(S) R(S) 45+12 What are the poles of the system? For r(t) output in the time-domain y(t) For r(t) = t, t output in the time-domain y(t) 1- 2- 1,t 0, use partial fraction expansion and inverse Laplace transform to find the 3- 0, use partial fraction expansion and inverse Laplace transform to find the

Answer 1

y(s) .5 R LS) 2. Roots oP Denomina tor 2. 2. ,or, - 2- So Polus are -3,-y b) イ

y (S) R IS) 2. 2. D c s 124=5 A 5 1 2-

.sl12-t (음 s-프.) yt 5)= 1 2. 12S s 35,2 ylssh hs ㄧㄥ -35 I 2 7) 25 -a t sta s+a

2. 2. 35/2 2o.S) y(s) s/n. = 2. 3 s 1 2. 3S 2. o. S) 12. 1 2- s.- "z e Sinhlo.st).

RCS+

B-S 12 - 72 月= -7(5 i44 Dー i4 1 1 2 135 3 5

七 185 l4 4 -245 28を I 녀녀 2. o.25 l 25 2. i44 1 2