Question

A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg, is made to support a mass of 60 kg. The spring and the mass system is displaced vertically through 12.5 mm and released. Determine the frequency of natural vibration of the system.

(a) 6 Hz

(b) 4.98 Hz

(c) 5.98 Hz

(d) none of the mentioned

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This question is from Centre of Percussion topic in section Simple Harmonic Motion of Machine Kinematics

Answer 1

Right answer is (b) 4.98 Hz

The best explanation: Given : m = 60 kg ; r = 12.5 mm = 0.0125 m ; x = 5 mm = 0.005 m

Since a mass of 1.5 kg extends the spring by 0.25 mm, therefore a mass of 60 kg will extend the spring by an amount,

δ = 0.25/1.5 x 60 = 10 mm = 0.01m

We know that frequency of the system,

n = 1/2π√g/δ = 1/2π√9.81/0.01 = 4.98 Hz.