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
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2. The harmonic motion is represented in terms of
a) square function
b) circular sine function
c) Circular function
d) Semicircular cosine function
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3. What is A1 in the equation x1 = A1 sin ωt ?
a) Displacement
b) Amplitude
c) Velocity
d) Angular velocity
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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
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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
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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

 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

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

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
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8. The period of motion is
a) 0.1 s
b) 0.09 s
c) 0.209 s
d) 0.3 s
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The period of motion T= (2Π/ 30) s
                      = 0.209 s

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

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
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           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
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Sanfoundry Global Education & Learning Series – Mechanical Vibrations.

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

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