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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/m^2. Determine the frequency of transverse vibrations of the shaft.

(a) 31

(b) 35

(c) 37

(d) 41

I have been asked this question in an interview for internship.

This question is from Natural Frequency of Free Transverse Vibrations topic in portion Longitudinal and Transverse Vibrations of Machine Dynamics

1 Answer

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by (38.6k points)
Right option is (d) 41

Easy explanation: We know that deflection is given by the relation:

Wl^3/3E.I

I = 0.3×10^-6 m^4

d = 0.147×10^-3

f = 0.4985/\(\sqrt{d}\)

Thus f = 41 Hz.

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