# Time Response Analysis MCQ

1. A second-order system with a zero at -2 has its poles located at -3 + j4 and -3 – j4 in the s-plane. The undamped natural frequency and the damping factor of the system respectively are

2. The transient response of the second-order underdamped system starting from rest is given by

c(t) = Ae-6t sin(8t + θ), t ≥ 0.

The natural frequency of the system is

1. 100
2. 10
3. 9
4. 8

3. The steady state response c(t) for an input r(t) = sin2t to a system transfer function $\frac{1}{s + 4}$ is

1. 0.632 cos2t
2. 0.316 sin(2t – 26.5°)
3. sin(2t – 45°)
4. 0.25 sin2t

4. For a critically damped system, the closed-loop poles are

1. real, unequal and negative
2. complex conjugate with negative real part
3. real, equal and negative
4. purely imaginary

5. The open-loop transfer function of a unity feedback system is $\frac{K}{s(s+4)}$. For a damping factor of 0.5, the value of the gain K must be set to

1. 16
2. 4
3. 2
4. 1

6. A system has a transfer function

$\frac{C(s)}{R(s)}=\frac{4}{s^2 + 1.6s + 4}$

For a unit step response and 2% tolerance band, the settling time will be

1. 2 seconds
2. 3 seconds
3. 4 seconds
4. 5 seconds

7. How many poles does the following function have?

$R(s)=\frac{s^3 + 2s + 1}{s^2 + 3s + 2}$

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

8. In a system, the damping coefficient is -2. The system response will be

1. Undamped
2. Oscillations with decreasing magnitude
3. Oscillations with increasing magnitude
4. Critically damped

9. Consider the following statements regarding the effect of adding a pole in the open-loop transfer function on the closed-loop step response:

1. It increases the maximum overshoot.
2. It increases the rise time.
3. It reduces bandwidth.

Which of the above statements are correct

1. i, ii and iii
2. i and ii only
3. i and iii only
4. ii and iii only

10. The derivative of a parabolic function becomes

1. a unit-impulse function
2. a ramp function
3. a gate function
4. a triangular function

11. In the time-domain specification, decay ratio is the ratio of the

1. amplitude of the first peak and the steady-state value
2. amplitudes of the first two successive peaks
3. peak value to the steady-state value
4. none of the above

12. Consider the time response of a second-order system with damping coefficient less than 1 to a unit step input:

1. It is overdamped.
2. It is a periodic function.
3. Time duration between any two consecutive values of 1 is the same.

Which of the above statements is/are correct?

1. i, ii and iii
2. i only
3. ii only
4. iii only

13. A sensor requires 30 s to indicate 90% of the response to a step input. If the sensor is a first-order system, the time constant is

[given, loge (0.1) = -2.3]
1. 15 s
2. 13 s
3. 21 s
4. 28 s

14. Consider the following input and system types:

 Input type System type Unit step Type ‘0’ Unit ramp Type ‘1’ Unit parabolic Type ‘2’

Which of the following statements are correct?

1. Unit step input is acceptable to all three types of system.
2. Type ‘0’ system cannot accept unit parabolic input.
3. Unit ramp input is acceptable to Type ‘2’ system only.
1. i and ii only
2. i and iii only
3. ii and iii only
4. i, ii and iii

15. The characteristic equation of a closed-loop system is s2 + 4s+ 16 = 0. The natural frequency of oscillation and damping constant respectively are

2. $2\sqrt{3} rad/s$ and $\frac{1}{\sqrt{3}}$

16. The unit impulse response of a system is given as c(t) = -4e-t + 6e-2t. The step response of the same system for t ≥ 0 is equal to

1. 3e-2t – 4e-t + 1
2. -3e-2t + 4e-t + 1
3. -3e-2t + 4e-t – 1
4. 3e-2t + 4e-t + 1

17. A unity feedback second-order control system characterized by the open-loop transfer function

$G(s) =\frac{K}{s(Js+ B)}$

J = moment of inertia, B = damping constant and K = system gain.

The transient response specification which is not affected by system gain variation is

1. Peak overshoot
2. Rise time
3. Settling time
4. Time to peak overshoot

18. For a unit step input, a system with forward path transfer function G(s) = 20/s2 and feedback path transfer function H(s) = (s+5) has a steady-state output of

1. 2
2. 0.5
3. 1
4. 0.2

19. Consider the open-loop transfer function:

$G(s)H(s) =\frac{5(s+1)}{s^2(s+5)(s + 12)}$

The steady state error due to a ramp input is

1. 0
2. 5
3. 12
$G(s)=\frac{50}{(1+0. 1s)(1+2s)}$ are respectively