Calculate time required to reach 2 of steady state value

Question

Question 1. A second order system has a transfer function given by 25/(s² + 8s + 25) if the system initially at rest is subject to a unit step input at t = Π/3. The second maximum overshoot occurs at

(A) Π/3 (B) 2Π/3 (C) Π (D) 4Π/3

Question 2. The closed loop transfer function is 4/(s+10)(s+100). Calculate time required to reach 2% of steady state value when input is u(t)

(A) 0.072 sec (B) 0.4 sec (C) 40 sec (D) 400 sec

Question 3. The block diagram of a closed loop control system is given by figure the values of k and p such that the system has a damping ratio 0.7 and an undamped natural frequency Z of 5 rad/sec, are respectively equal to

(A) 20 and 0.3 (B) 20 and 0.2 (C) 25 and 0.3 (D) 25 and 0.2

Question 4. If the open loop transfer function of a negative feedback control system is G(s)H(s) = k/(s+1)³, then the gain k for a closed loop pole at (-1/2  + j√3/2) is ________.