Question

Problem #3 Knowing G(S) 2+2anS+wh Drive the Second Order System's response y(t) and Steady State Response yss to the Ramp Input u(t) t, for each one of these cases. A. Not Damped B. Critically Damped C. Over Damped D. Under Damped Partial fraction expansion for sections C and D is the same and is provided in the lecture notes

please solve all parts

Answer 1

UH)inkut 0Utput Solution y- Taking Lathe Ul) 2 Caly Y 2. C S+D Srdgonsto S ts2dreaf/+ [Cs+D) S2 Asts22po 2 R tC 0: 960nAts tD A 2 SY 24 C2 42 -25 Aos 01erdambed G1) 2 15 2

+ S+EwA Takfing inverse lalee gnt tt wn (n Por Underdanbed 1) S+fejTREn) s+fn)-241 L = Gal n fom 0 r 221 St-Gn Taking inverse laplace e @n +at0 tO-oD Gon

la Critically dated 1 $22t0nStn 2 S+wnj2 From Tasn Sy -2 2 Stn) Stan Ta king inverse lablaie Ceat Lunt -2 Lin dt t7s 0 Not Darted A from y= S2 Ta kung nverse Lakace t t sinent Sinut