Time Response Analysis MCQ

41. The impulse response of a second-order underdamped system started from rest is given by

c(t) = 12.5 e^-6t sin 8t, t ≥ 0

What are the natural frequency and the damping factor of the system respectively?

1. 10 and 0.8
2. 10 and 0.6
3. 8 and 0.8
4. 8 and 0.6

42. A unity feedback system with open-loop transfer function of $\frac{20}{s(s+5)}$ is excited by a unit step input. How much time will be required for the response to settle within 2% of the final desired value?

1. 1.60 sec
2. 0.25 sec
3. 4.00 sec
4. 2.40 sec

43. Consider the following:

1. Rise time
2. Settling time
3. Delay time
4. Peak time

What is the correct sequence of the time domain specifications of a second-order system in the ascending order of the values?

1. ii, iv, i, iii
2. iii, iv, i, ii
3. ii, i, iv, iii
4. iii, i, iv, iii

44. In a fluid flow system two fluids are mixed in an appropriate proportion. The concentration at the mixing point is y(t) and it 1s reproduced without change. T_d seconds later at the monitoring point as b(t). What is the transfer function between b(t) and y(t)? (Where S is distance between monitoring point and mixing point)

1. e^-T_d
2. e^+T_ds
3. e^-T_ds
4. e^+T_d

45. The response of an initially relaxed, linear constant parameter network to a unit impulse applied at t= 0 is 4e^-2t u(t). What is the response of this network to the unit step function?

1. 2(1 – e^-2t) u(t)
2. 4(e^-t – e^-2t) u(t)
3. sin2t
4. (1 – 4e^-4t) u(t)

46. A second-order system has a natural frequency of oscillations of 3 rad/sec and damping ratio of 0.5. What are the values of resonant frequency and resonant peak of the system?

1. 1.5 rad/sec and 1.16
2. 1.16 rad/sec and 1.5
3. 1.16 rad/sec and 2.1
4. 2.1 rad/sec and 1.16

47. A control system has an open-loop transfer function

$\frac{K(1+0.5s)(1+2s+5s^2)}{s^2(1+s)(1+5s+10s^2)(1+100s+500s^2)}$

What is the type of the system?

1. 0
2. 1
3. 2
4. 3

48. Which one of the following is correct?

Final value theorem is not applicable for the system when the input is

1. ramp
2. step
3. parabolic
4. exponential

49. Which one of the following statements regarding steady-state errors in control system is not correct?

1. Steady-state error analysis relies on the use of initial value theorem.
2. Steady-state error is a measure of system accuracy when a specific type of input is applied to a control system.
3. The error constants do not give information regarding steady-state error when inputs are other than step, ramp and parabolic.
4. Steady-state error does not provide information on how the error varies with time.

50. Which one of the following is the most likely reason for large overshoot in a control system?

1. High gain in a system
2. Presence of dead time delay in a system
3. High positive correcting torque
4. High retarding torque