Question

the given figure, considering left end has one rotor, If the mass moment of inertia of the shaft till node N1 is increased to four times, then what will be the effect on free torsional vibrations of a rotor at left end of N1?

(a) Increases 4 times

(b) Increases 2 times

(c) Decreases 4 times

(d) Decreases 2 times

The question was asked by my college director while I was bunking the class.

I'm obligated to ask this question of Free Torsional Vibrations of a Three Rotor System topic in division Torsional Vibrations of Machine Dynamics

Answer 1

Correct answer is (d) Decreases 2 times

To explain I would say: If N1 is the node then left end and N1 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.