+1 vote
in Machine Dynamics by (34.3k points)
A cantilever shaft having 50 mm diameter and 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. Calculate the natural longitudinal frequency in Hz.

(a) 575

(b) 625

(c) 525

(d) 550

The question was asked during an internship interview.

Enquiry is from Natural Frequency of Free Longitudinal Vibrations in chapter Longitudinal and Transverse Vibrations of Machine Dynamics

1 Answer

0 votes
by (38.6k points)
The correct choice is (a) 575

The best I can explain: Area = πd^2/4 = 0.00196 m^2

s = W.l/A.E = = 0.751 µm

I = 0.3×10^-6 m^4

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

  = 575 Hz.

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