Question

In the given figure, considering PN as one shaft, If the mass moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a rotor at P?

(a) Increases 4 times

(b) Increases 2 times

(c) Decreases 4 times

(d) Decreases 2 times

This question was posed to me in a national level competition.

This interesting question is from Free Torsional Vibrations of a Two Rotor System in chapter Torsional Vibrations of Machine Dynamics

Answer 1

The correct answer is (d) Decreases 2 times

Best explanation: If N is the node then PN can be considered as a shaft of single rotor system, since the free torsional vibrations of a single motor system depends on the inverse of square root of the mass moment of inertia of the system, increasing 4 times will lead to decrease in two times the initial vibration.