# Dynamic behaviour of first order and second order systems Objective Questions and Answers

1. In a second order system, the damping factor is 0.65 and the natural frequency is 4 Hz. If the stiffness of springs is halved, the new values of damping factor and natural frequency are _______
a) 0.92, 2.83 Hz
b) 0.46, 5.66 Hz
c) 0 92, 5.66 Hz
d) 0.46, 2.83 Hz.
2. The volume of bulb of a liquid filled thermometer is 1000 mm3. Its time constant and sensitivity are respectively 300 s and 3.6 mm/°C. If the volume of the bulb is reduced to 500 mm3, the sensitivity becomes ______________
a) 7.2 mm/°C
b) 10.8 mm/°C
c) 1.8 mm/°C
d) 1.2 mm/°C if other conditions remain the same.
3. In force-current analogy stiffness constant K is analogous to __________
a) inductance
b) reciprocal of inductance
c) capacitance
d) reciprocal of capacitance
4. Dynamic response consists of __________
a) two parts, one steady state and the other transient state response
b) only transient state response
d) steady state and transient frequency response
Answer: two parts, one steady state and the other transient state response
5. In force-voltage analogy viscous friction constant B is analogous to __________
a) resistance
b) reciprocal of resistance
c) inductance
d) capacitance
6. An RC series circuit has a resistance of 2 MÎ© and a capacitance of 1ÂµF. It is subjected to a step input of 10 V. The dynamic error (reference to voltage across capacitor) at time t = 4 s of application of input is __________
a) 1.35 V
b) 0.5 V
c) 3.68 V
d) 0 V
7. An undamped second order instrument has a natural frequency of 500 Hz. It is subjected to a sinusoidal input of unit amplitude at 500 Hz. The amplitude of output is __________
a) unity
b) 0.5
c) 2.0
d) Infinity.
8. The transfer function of a system is defined as __________
a) ratio of Laplace transform of input to Laplace transform of output with initial conditions not equal to zero.
b) ratio of Laplace transform of output to Laplace transform of input with initial conditions not equal to zero.
c) ratio of Laplace transform of input to Laplace transform of output with all initial conditions equal to zero.
d) ratio of Laplace transform of output to Laplace transform of input with all initial conditions equal to zero.
Answer: ratio of Laplace transform of output to Laplace transform of input with all initial conditions equal to zero.
9. The following are the desirable dynamic characteristics of a measurement system  _______
a) fast response, fidelity, measuring lag and dynamic error
b) fast response and measuring lag
c) fidelity and measuring lag
d) fast response and fidelity
10. A first order system is subjected to a step input. Its time constant can be defined as __________
a) time for the output to rise to 63.2% of its final steady value in the case of rising output.
b) time for the output to drop to 36.8% of its initial value in the case of a decaying output.
c) time for output to rise (in case of rising output) and decrease to (in case of a decaying output) reach its final steady value if the initial rate of change of output is maintained
d) all of the above
11. In thermal systems if M is mass of liquid stored, Q is the liquid inflow rate and s is the specific heat, the thermal resistance is given by __________
a) Ms
b) Qs
c) 1/Ms
d) 1/Qs
12. A first order system has a time constant of 20 s. It is subjected to a step input. The settling time of the output is assumed to be the time it reaches 95% of its final steady state value. The settling time of the system is __________
a) 100 s
b) 60 s
c) 20 s
d) infinity
13. Bandwidth, a frequency domain concept, is indicative of __________
a) rise time in time domain
b) settling time in time domain
c) steady state error in the domain
d) all of the above.
Answer: settling time in time domain
14. The volume of bulb of a liquid filled thermometer is 1000 mm3. Its time constant is 300 s. It is desired to reduce the time constant 100 s. What is the new volume of the bulb, if all other conditions remain the same except the dimensions of the bulb __________
a) 333.3 mm3
b) 37 mm3
c) 10 mm3
d) 577 mm3
15. A 2 gm mass is suspended from a simple spring. The deflection caused is 5 mm. The natural frequency of the system is
a) 7 Hz
b) 22 Hz
c) 2.2 Hz
d) none of the above.
16. In a second order system, the steady state error is 0.02. If both viscous friction constant and spring constant are doubled, the steady error will be __________
a) 0.01
b) 0.04
c) 0.0025
d) 0.02.
17. In second order system, the frequency of damped oscillations is 18 rad/s. The value of damping factor 0.866. The natural frequency of oscillations is __________
18. In a second order system, the peak overshoot is 100%. The value of damping factor is __________
a) 1
b) 0.707
c) 0
d) 0.5.
19. In order that a first order instrument should indicate an output which is within ± 10% of the true value of the output when subjected to a sinusoidal input the product Ï‰Ï„, where Ï‰ = angular frequency of input and Ï„ = time constant of instrument should be __________
a) less than 0.5
b) greater than 0.5
c) less than 10
d) greater than 10.
20. A second order underdamped system has a damping factor of 0.8. It is subjected to a sinusoidal input of unit amplitude. It has resonant peak of __________
a) 108%
b) 92%
c) 20%
d) it has no resonant peak.
Answer: it has no resonant peak.
21. A second order system when subjected to a unit step input has a peak overshoot of 10%. The same system when subjected to a sinusoidal input of unit amplitude will have a resonant peak of nearly
a) 103%
b) 110%
c) 190%
d) none of the above.
22. A first order thermometer has a time constant of 50 s. It is subjected to a sinusoidal input cycling at 0.002 Hz. The time lag of the instrument is __________
a) 50 s
b) 44.6 s
c) 500 s
d) 0.01 s.
23. A quantity whose magnitude has a definite repeating time cycle is called a __________
a) transient
d) transient state periodic
24. In liquid level systems, the units of capacitance of a tank are __________
a) m2
b) m3
c) m2/s
d) m-2s