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Bounded Rotational Oscillation

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A uniform disk, initially at rest, is subjected to a time-varying torque described by the equation τ(t)=τ0sin⁡(ωt)\tau(t) = \tau_0 \sin(\omega t). Under which of the following conditions will the disk’s angular velocity oscillate with a bounded amplitude instead of increasing indefinitely?

A

A torque opposing motion that is proportional to angular velocity acts

B

The initial torque amplitude τ0\tau_0 is very small

C

The frequency of applied torque matches the disk’s natural frequency

D

The disk’s moment of inertia increases and decreases with time

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