Question

The natural frequency of a spring-mass system on earth is ωn. The natural frequency of this system on the moon (gmoon = gearth/6) is

(a) ωn

(b) 0.408ωn

(c) 0.204ωn

(d) 0.167ωn

I had been asked this question in unit test.

This interesting question is from Types of Vibratory Motion and Natural Frequency of Free Longitudinal Vibrations in division Longitudinal and Transverse Vibrations of Machine Dynamics

Answer 1

The correct choice is (a) ωn

The explanation is: We know natural frequency of a spring mass system is,

ωn = √k/m                       ………..(i)

This equation (i) does not depend on the g and weight (W = mg)

So, the natural frequency of a spring mass system is unchanged on the moon.

Hence, it will remain ωn , i.e. ωmoon = ωn.