# Mechanical Vibrations Questions and Answers – Harmonic Motion

This set of Mechanical Vibrations Multiple Choice Questions & Answers (MCQs) focuses on “Harmonic Motion”.

1. Harmonic motion is one of the form of periodic motion
a) Yes
b) No
View Answer

Answer: c
Explanation: A periodic motion repeats itself after an equal interval of time. The simplest type of periodic motion is Harmonic motion.

2. The harmonic motion is represented in terms of
a) square function
b) circular sine function
c) Circular function
d) Semicircular cosine function
View Answer

Answer: b
Explanation: The harmonic motion is represented in terms of circular cosine and sine functions. All harmonic motions are periodic in nature.

3. What is A1 in the equation x1 = A1 sin ωt ?
a) Displacement
b) Amplitude
c) Velocity
d) Angular velocity
View Answer

Answer: b
Explanation: Harmonic motion is represented in terms of circular sine function. In the equation x1 = A1 sin ωt, x1 is the displacement and A1 the amplitude.
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4. The acceleration in a simple harmonic motion is always proportional to
a) its displacement
b) its velocity
c) its Angular velocity
d) its amplitude
View Answer

Answer: a
Explanation: The acceleration in a simple harmonic motion is always directed towards a particular fixed point and proportional to its displacement.

5. Which of the following is an example of a simple harmonic motion ?
a) x1 = A1 cos ωt
b) x1 = A1 tan ωt
c) x1 = A1 sec ωt
d) x1 = A1 cosec ωt
View Answer

Answer: a
Explanation: Harmonic motion is represented in terms of circular cosine and sine function. The motion gives by x1 = A1 cos ωt is an example of a simple harmonic motion.

6. If the two harmonic motions of amplitudes A1 and A2 , the same frequency ɷ and phase difference φ as x1 = A1 sin ɷt and x2 = A2 sin ( ɷt + φ ), then resultant motion is——
a) sin ɷt ( A1 – A2 cos φ ) + A2 cos ɷt sin φ
b) sin ɷt ( A1 + A2 cos φ ) + A2 cos ɷt sin φ
c) cos ɷt ( A1 + A2 cos φ ) + A2 cos ɷt sin φ
d) sin ɷt ( A1 + A2 cos φ ) + A2 sin ɷt sin φ
View Answer

Answer: b
Explanation: x1 = A1 sin ɷt and x2 = A2 sin ( ɷt + φ ), the resultant motion is given by adding x1 and x2

``` x = x1 +  x2  =  A1 sin ɷt + A2 sin ( ɷt +  φ )
=  A1  sin ɷt +  A2 (sin  ɷt cos φ + sin  φ cos ɷt )
=  sin ɷt ( A1 + A2 cos φ ) + A2 cos ɷt sin  φ```

Common data question from 7 to 12

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Given harmonic motion is x (t) = 0.003 cos ( 30t ) + 0.004 sin (30t) m

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7. The amplitude of motion for given harmonic motion is
a) 0.001 m
b) 0.003 m
c) 0.004 m
d) 0.005 m
View Answer

Answer: d
Explanation: Amplitude of motion X = √(0.0032 + 0.0042)m
= 0.005 m

8. The period of motion is
a) 0.1 s
b) 0.09 s
c) 0.209 s
d) 0.3 s
View Answer

Answer: c
Explanation:

```The period of motion T= (2Π/ 30) s
= 0.209 s```
9. The frequency in hertz is
a) 5.77 Hz
b) 4.77 Hz
c) 2.77 Hz
d) 3.77 Hz
View Answer
Answer: b
Explanation:

```frequency f = (1/T)
= (1/0.209)
= 4.77 Hz```

10. The frequency in rad/s is
a) 10 rad/s
b) 20 rad/s
c) 30 rad/s
d) 40 rad/s
View Answer

Answer: c
Explanation:

```frequency in rad/s ɷ = 2Πf
= 30 rad/s```

11. The frequency in revolution per minute is
a) 181 rpm
b) 171 rpm
c) 161 rpm
d) 191 rpm
View Answer

Answer: d
Explanation:

```           ɷ = ( 20 rad/s )
= ( 1/2Π ) ( rev/rad )
= ( 60/1 )  ( s/min )
= 191.0 rpm```

12. The phase angle is
a) 0.765 rad
b) 0.833 rad
c) 0.643 rad
d) 0.903 rad
View Answer

Answer: c
Explanation: φ = tan-1(0.003/0.004)
= 0.643 rad

Sanfoundry Global Education & Learning Series – Mechanical Vibrations.

To practice all areas of Mechanical Vibrations, 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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