218. The unit step response of a second order linear system with zero initial states is given by c (t) = 1 + 1.25 exp (-6t) sin (8t - tan-1 1.333); t > 0 The damping rafio and the undamped natural frequency of oscillation of the system are respectively

A. 0.6 and 10 rad/s

B. 0.6 and 12.5 rad/s

C. 0.8 and 10 rad/s

D. 0.8 and 12.5 rad/s

219. Which one of the following statements regarding the state transmition matrix is correct?

A. 0(0) = 0

B. 0-1 (t) = ()

C. 4)(t1 + t2) = 4?(t1) + 0(t2)

D. 002 - ti) 4)(t1 - to) = 4)(t2 - to)

220. A control system whose step response is 0.5 (1 + e-2t) is cascaded to another control block whose impulse response is e4. The transfer function of the cascaded combination is

A.150

B. 30?

C.450

D.600

221. The characteristic equation of a closed loop control system is given by 52 + 9s + 16 = 0. The resonant frequency in radians/sec of the system is

A.2

B. 2?IF

C.4

D. 413-

222. For a unit step input, a system with forward path transfer, function G(s)20= -7 and feedback path transfer function H(s) = (s + 5) has a steady state output of

A.20

B.5

C.0.2

D. zero

223. The transfer function of a multi-input multi-output system with the state-space representation of X = AX + BU Y = CX + DU where X represent at state, Y the output and U the input vector, will be given by

A. C(s1 - A)'

B. C(s1 -

C. (sI - A)-1 B + D

D. C(s1 - A)-1 B

224. The unit impulse response of a unit feedback control system is given by c(t) = -e-t + 2e-t (t > 0) The open-loop transfer function is equal to

A. s + 1(2s + 1)

B. (s + 2)2

C. (s + 1)2

D.s + 1(s +0)2

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