Machine Dynamics Questions and Answers – Natural Frequency of Free Transverse Vibrations

This set of Machine Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Natural Frequency of Free Transverse Vibrations”.

1. A cantilever shaft having 50 mm diameter and a length of 300 mm has a disc of mass 100 kg at its free end. The Young’s modulus for the shaft material is 200 GN/m2. Determine the frequency of transverse vibrations of the shaft.
a) 31
b) 35
c) 37
d) 41
View Answer

Answer: d
Explanation: We know that deflection is given by the relation:
Wl3/3E.I
I = 0.3×10-6 m4
d = 0.147×10-3
f = 0.4985/\(\sqrt{d}\)
Thus f = 41 Hz.

2. For the same dimensions of a beam, transverse vibrations have a lower frequency than longitudinal frequency.
a) True
b) False
View Answer

Answer: a
Explanation: Keeping the dimensions of the testing beam same, it is noted that the natural frequency of vibrations obtained in longitudinal waves is larger than the one obtained in transverse waves.

3. A cantilever shaft having 50 mm diameter and a length of 300 mm has a disc of mass 100 kg at its free end. The Young’s modulus for the shaft material is 200 GN/m3. Determine the static deflection of the shaft in mm.
a) 0.147
b) 0.213
c) 0.132
d) 0.112
View Answer

Answer: a
Explanation: We know that deflection is given by the relation:
Wl3/3E.I
W = 100xg, l=0.3m, I = I = 0.3×10-6 m4
substituting values we get d = 0.147mm.
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4. For the same dimensions of the shaft which of the following has the greater natural frequency?
a) Transverse
b) Longitudinal
c) Depends on thickness
d) Depends upon length
View Answer

Answer: b
Explanation: If the dimensions of the testing beam are kept same, it is observed that the natural frequency of vibrations obtained in longitudinal waves is larger than the one obtained in transverse waves.

5. Calculate the natural frequency of transverse vibrations if the static deflection is 0.01mm.
a) 157.6
b) 144.8
c) 173.2
d) 154.1
View Answer

Answer: a
Explanation: We know that the natural Frequency of Free Transverse Vibration is given by the equation
f = 0.4985/\(\sqrt{s}\)
where s is the displacement of the spring.
substituting the given values we get
f=157.6 Hz.
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6. Increasing mass will result in lower frequency.
a) True
b) False
View Answer

Answer: a
Explanation: We know that deflection is given by the relation :
Wl3/3E.I
Increasing the mass will result in an increased deflection which, frequency decreases as the deflection increases hence increasing mass will reduce the frequency of vibration.

7. Calculate the static deflection in µm of transverse vibrations if the frequency is 200Hz.
a) 6
b) 0.6
c) 60
d) 0.006
View Answer

Answer: a
Explanation: We know that the natural Frequency of Free Transverse Vibration is given by the equation
f = 0.4985/\(\sqrt{s}\)
where s is the displacement of the spring.
substituting the given values we get
f = 0.00000621255625‬ m.

Sanfoundry Global Education & Learning Series – Machine Dynamics.

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To practice all areas of Machine Dynamics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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