# Undamped and Damped Free Vibrations - Mechanical Engineering (MCQ) questions and answers

1)   Calculate logarithmic decrement if damping factor is 0.33.

a. 1.36
b. 3.23
c. 5.16
d. 2.19
 Answer  Explanation ANSWER: 2.19 Explanation: No explanation is available for this question!

2)   Calculate coefficient of viscous damper, if the system is critically damped.
Consider the following data:

1. Mass of spring mass damper system = 350 kg
2. Static deflection = 2 x 10–3 m
3. Natural frequency of the system = 60 rad/sec

a. 100.5 x 103 N-s/m
b. 80 x 103 N-s/m
c. 42 x 103 N-s/m
d. None of the above
 Answer  Explanation ANSWER: 42 x 103 N-s/m Explanation: No explanation is available for this question!

3)   Determine logarithmic decrement, if the amplitude of a vibrating body reduces to 1/6th in two cycles.

a. 0.223
b. 0.8958
c. 0.3890
d. None of the above
 Answer  Explanation ANSWER: 0.8958 Explanation: No explanation is available for this question!

4)   Determine natural frequency of a system, which has equivalent spring stiffness of 30000 N/m and mass of 20 kg?

a. 12.32 Hz
b. 4.10 Hz
c. 6.16 Hz
d. None of the above
 Answer  Explanation ANSWER: 6.16 Hz Explanation: No explanation is available for this question!

5)   Calculate natural frequency of damped vibration, if damping factor is 0.52 and natural frequency of the system is 30 rad/sec which consists of machine supported on springs and dashpots.

6)   In damped free vibrations, which parameters indicate vibrations?

a. Natural frequency
b. Rate of decay of amplitude
c. Both a. and b.
d. None of the above
 Answer  Explanation ANSWER: Both a. and b. Explanation: No explanation is available for this question!

7)   According to D' Alembert's principle, m (d2x/ dt2) + c (dx/dt) + Kx =0 is the differential equation for damped free vibrations having single degree of freedom. What will be the solution to this differential equation if the system is critically damped?

a. x = (A + Bt) e– ωt
b. x = X e– ξωt (sin ωdt + Φ)
c. x = (A – Bt) e– ωt
d. x = X e– ξωt (cos ωdt + Φ)
 Answer  Explanation ANSWER: x = (A + Bt) e– ωt Explanation: No explanation is available for this question!

8)   Which of the following statements is/are true for coulomb damping?

1. Coulomb damping occurs due to friction between two lubricated surfaces
2. Damping force is opposite to the direction of motion of vibrating body
3. For smooth surfaces, coefficient of friction depends upon velocity
4. Damping force depends upon the rubbing velocity between two rubbing surfaces

a. Only statement 1
b. Statement 2, 3 and statement 4
c. Only statement 2
d. All the above statements are true
 Answer  Explanation ANSWER: Only statement 2 Explanation: No explanation is available for this question!

9)   What is meant by critical damping coefficient?

a. Frequency of damped free vibrations is less than zero
b. The motion is aperiodic in nature
c. Both a. and b.
d. None of the above
 Answer  Explanation ANSWER: The motion is aperiodic in nature Explanation: No explanation is available for this question!

10)   Which of the following relations is true for viscous damping?

a. Force α relative displacement
b. Force α relative velocity
c. Force α (1 / relative velocity)
d. None of the above
 Answer  Explanation ANSWER: Force α relative velocity Explanation: No explanation is available for this question!

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