# Earthquake Engineering Questions and Answers – Free Vibration Analysis of SDOF System

This set of Earthquake Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Free Vibration Analysis of SDOF System”.

1. Which of the following is not a constituent of a vibrating system?
a) Mass element (m)
b) Spring element (k)
c) Velocity element (v)
d) Dashpot (c)
View Answer

Answer: c
Explanation: Velocity element is not a constituent of a vibrating system. The mass element (m) stores the kinetic energy and it is also responsible for generation of inertia forces. The spring element (k) stores the potential energy and it is responsible for generation of elastic restoring forces. The dashpot (c) represents the damper for dissipation or loss of energy.

2. Which of the following statement is true for vibration?
a) Vibration is a linear motion of a body or a particle about a reference point
b) Vibration is a projectile motion of a body or a particle about a reference point
c) Vibration is a tangential motion of a body or a particle about a reference point
d) Vibration is an oscillatory motion of a body or a particle about a reference point
View Answer

Answer: d
Explanation: Vibration is an oscillatory motion of a body or a particle about a reference point. The oscillations may be random or periodic. The oscillatory motion may be sinusoidal (harmonic) or non-sinusoidal (complex). The effect of inertia of any vibrating body comes into the picture by virtue of Newton’s second law of motion.

3. What do you call a system having the value of damping ratio equal to 1?
a) Undamped
b) Critically damped
c) Under-damped
d) Over-damped
View Answer

Answer: b
Explanation: Damping ratio is the ratio of actual damping coefficient to the critical damping coefficient. The value of damping ratio is 1 for a critically damped system. When damping ratio is zero, the system is an undamped system. For an under-damped system, the damping ratio ranges between 0 and 1. For over-damped system, the damping ratio is greater than 1.
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4. What type of roots are obtained for the overdamped case?
a) Independent of the type of case
b) Non-real roots
c) Real and negative
d) Real and positive
View Answer

Answer: c
Explanation: The value of damping ratio (zeta) is greater than 1 in overdamped case. Two distinct, negative real roots are obtained. These roots can be determined from the initial conditions. The system returns to the zero-position or the equilibrium position very slowly in comparison to the critically damped and underdamped case.

5. What is the unit of damping ratio (zeta)?
a) radian/second
b) Unit less
c) N/s
d) N/m/s
View Answer

Answer: b
Explanation: The damping ratio (zeta) is a ratio of actual damping coefficient (C) to the critical damping coefficient (Cc). As both numerator and denominator has same units, the damping ratio is unit less. It is a dimensionless quantity.

6. For which of the following case, the nature of motion is oscillatory with a decaying amplitude?
a) Underdamped
b) Critically damped
c) Overdamped
d) Undamped
View Answer

Answer: a
Explanation: For the underdamped case, the motion is of oscillatory nature whose amplitude decreases with time. In such condition the damping of an oscillator causes it to return to equilibrium with a decaying amplitude. The system returns to equilibrium faster but exceeds and crosses the equilibrium position more than one time.

7. A load whose magnitude and/or position and/or direction changes with respect to time is called as dynamic load.
a) True
b) False
View Answer

Answer: a
Explanation: Dynamic load is a load in which magnitude, direction and position change with respect to time. While carrying out dynamic analysis we need to consider the dynamic loads. The internal forces generated, reactions, deflections etc. that are generated because of these dynamic loads are also dependent on time.
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8. What is the value of frequency (F) if the natural time period (T) is 0.2 seconds?
a) 0.2 Hz
b) 1 Hz
c) 2 Hz
d) 5 Hz
View Answer

Answer: d
Explanation: Given,
Natural time period (T) = 0.2 seconds
Frequency = 1/T
= (1/0.2) second-1
= 5 Hz or 5 second-1

9. What is the value of natural time period (T) if the natural circular frequency (ω) is 30 rad/sec?
a) 0.067 sec
b) 0.033 sec
c) 0.209 sec
d) 0.105 sec
View Answer

Answer: c
Explanation: Given,
natural circular frequency (ω) = 30 rad/sec
Natural time period (T) = 2π / ω
= 2π / 30
= 0.209 sec
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10. What is the range of damping ratio (zeta) for the system to be termed as underdamped?
a) 0 ≤ zeta ≤ 1
b) 0 < zeta < 1
c) 0 < zeta ≤ 1
d) 0 ≤ zeta < 1
View Answer

Answer: b
Explanation: For any system to be termed as underdamped system, the range of damping ratio should be between 0 and 1. When damping ratio is zero, the system is an undamped system. The value of damping ratio is 1 for a critically damped system. For over-damped system, the damping ratio is greater than 1.

Sanfoundry Global Education & Learning Series – Earthquake Engineering.

To practice all areas of Earthquake Engineering, here is complete set of Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

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