If the polar moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a single motor system?

If the polar moment of inertia is increased to four times, then what will be the effect on free torsional vibrations of a single motor system? Correct Answer Increases 2 times

Since the free torsional vibrations of a single motor system depend on the square root of the polar moment of inertia of the system, increasing 4 times will lead to increase in two times the initial vibration.

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The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft and $$I$$ = Mass moment of inertia of the disc attached at the end of a shaft)