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

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

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

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.

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

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

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

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

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.

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