# Earthquake Engineering Questions and Answers – Vibration Isolation

This set of Earthquake Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Vibration Isolation”.

1. How does the magnitude of a harmonic force varies?
a) Logarithmically
b) Semi-logarithmically
c) Sinusoidally
d) Linearly

Explanation: Harmonic force is a force whose magnitude varies Sinusoidally with the time. Magnitude of the force will vary in accordance to the sine function. F=7sin(5t) N is an example of harmonic force which has magnitude 0 N at time = 0 sec and 7 N at time = pi/10.

2. The transmissibility ratio curves for all damping ratios intersect at which of the following value of tuning ratio (η)?
a) η = 1
b) η = 0
c) η = 3.14
d) η = 1.414

Explanation: The transmissibility ratio curves for all damping ratios intersect each other at η = √2 = 1.414 for TR=1. The transmissibility ratio is defined as the ratio of amplitude of the force transmitted to the support of the amplitude of the applied harmonic force.

3. For the harmonic force equation F = 8 Sin(3t) N, what is the magnitude of force for time equal to π/4?
a) 3.356 N
b) 5.657 N
c) 4.529 N
d) 6.752 N

Explanation: Given,
F = 8 Sin(3t) N
t = π/4
F = 8 Sin(3*π/4) = 5.657 N

4. What is closely resembled by the response of oscillator to a pulse of very short duration?
a) Free vibration response of oscillator due to non-zero initial velocity
b) Free vibration response of oscillator due to zero initial velocity
c) Forced vibration response of oscillator due to non-zero initial velocity
d) Forced vibration response of oscillator due to zero initial velocity

Explanation: The free vibration response of oscillator due to non-zero initial velocity is closely resembled by the response of oscillator to a pulse of very short duration. The duration is considered to be short with respect to natural time period. It can be used to derive analytical procedures for computing dynamic response of oscillators for arbitrary loadings.

5. Which of the following is a phenomenon in which a dynamic force drives a structure to vibrate at its natural frequency?
a) Damping
b) Resonance
c) Attenuation
d) Acceleration

Explanation: Resonance is a phenomenon in which a dynamic force pushes a structure to vibrate at its natural frequency. A small force can produce a large vibrational response if the structure is in resonance. When a physical object is acted upon by a dynamic force, it will start to vibrate. For a structure in resonance, a higher amplitude of vibration response is generated.

6. What is transmissibility ratio (TR)?
a) Ratio of amplitude of the force transmitted to the support of the amplitude of the applied harmonic force
b) Ratio of the support of the amplitude of the applied harmonic force to the amplitude of the force transmitted
c) Ratio of amplitude of the force loss to the support of the amplitude of the applied harmonic force
d) Ratio of the support of the amplitude of the applied harmonic force to the amplitude of the force loss

Explanation: The transmissibility ratio is defined as the ratio of amplitude of the force transmitted to the support of the amplitude of the applied harmonic force. The transmissibility ratio curves for all damping ratios intersect each other at η = √2 = 1.414 for TR=1.

7. Stiff isolators/mounting pads are preferred over flexible isolators.
a) False
b) True

Explanation: Stiff isolators or mounting pads (η < √2) are mostly preferred over flexible isolators (η > √2). There is excessive displacement of the machine frame itself in case of the flexible isolator, which creates hindrance in its operation. More damping is added to the system which improves the performance of vibration isolators.

8. For which value of tuning ratio, the amplitude of transmitted force is always smaller than the amplitude of imposed harmonic force?
a) η > 5
b) η = √2
c) η < √2
d) η > √2

Explanation: For tuning ratio η > √2, the amplitude of transmitted force is always smaller than the amplitude of imposed harmonic force. The flexible isolators have η > √2 with very small damping so that the amplitude of transmitted force has minimum isolation problem. Adding more damping to the isolator system is not advantageous for the vibration isolation.

9. What is the value of stiffness (k) if the natural circular frequency (ω) is 25 rad/sec and mass is 0.5 kg?
a) 12.5 N/m
b) 50 N/m
c) 312.5 N/m
d) 625 N/m

Explanation: Given,
Natural circular frequency (ω) = 25 rad/sec
Mass (m) = 0.5 kg
Natural circular frequency (ω) = √(k/m)
Stiffness (k) = m * ω2
= 0.5 * 252
= 312.5 N/m

10. What is the relation between the amplitude of the transmitted force and the amplitude of imposed harmonic force for η < √2?
a) Amplitude of the transmitted force < amplitude of imposed harmonic force
b) Amplitude of the transmitted force > amplitude of imposed harmonic force
c) Amplitude of the transmitted force = amplitude of imposed harmonic force
d) Amplitude of the transmitted force is independent of amplitude of imposed harmonic force

Explanation: For η < √2, the amplitude of transmitted force is greater than the amplitude of imposed harmonic force. The stiff isolators have η < √2 and has considerable amount of damping so that the machine frame does not vibrate due to excessive displacement. If more damping is added to the mounting system, it further reduces the amplitude of transmitted force.

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]