Question

While calculating the natural frequency of a spring-mass system, the effect of the mass of the spring is accounted for by adding X times its value to the mass, where X is

(a) 1/2

(b) 1/3

(c) 1/4

(d) 3/4

This question was addressed to me in unit test.

My enquiry is from Types of Vibratory Motion and Natural Frequency of Free Longitudinal Vibrations topic in portion Longitudinal and Transverse Vibrations of Machine Dynamics

Answer 1

Correct answer is (b) 1/3

The best explanation: Velocity at a distance “y” from fixed End = Velocity at free end /length of spring x y

∆k = 1/2 x M/3 x v^2.