Question

Referring to the system shown in Figure (a), determine the values of K and k such that the system has a damping ratio 5 of 0.7 and an undamped natural frequency wn of 4 radsec. R(S) C(s) K S + 2 k Select one: O a. K=0.249 and k=0.178 O b. K = 16 and k=0.225 Oc. K=0.467 and k=0.874 O d. K = 0.367 and k=12 O e. K=12 and k=18

Answer 1

K ces) Ris) ♡ S+2+k2 ces) RIS) k S[ S+2+x2] (cs) Res) s(s+2+12) k It S15+2+2) $ s(s+2+ 2) +k ces) k = RLS) s²+ 3 (2+k2)+k By comparing the above transfer function with Standard second ordof fonction, wav s²+2qwn stunt les Scanned with CamScanner

wow= kwnrk. 2.&.con 2+k2 2762 2 tk 11 ş- 2 K 2. Wn Given that f = 0.7 wn= 4 rad/sec wnuk k = won K = 162 16/2 k = 16. when wn= ustad see = K = 16. when &= 0.7 2x0.7 x 4 x 4 = 2 2+k2 k? 8x0.7-2 K²= 3.6 13.6 ko 1.8973 CS Scanned with CamScanner
note:- for a given value of zeta=0.7, the value of k is found to be 1.89 but it is not in the options