The motion of a torsional pendulum is (a) periodic
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The Tortional Pendulum and Moment of Inertia. A torsional pendulum, or torsional oscillator, consists of an extended mass suspended from a thin rod or wire. When the mass is twisted about the axis of the wire, the wire exerts a torque on the mass, tending to rotate it back to its original position.
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Since, it is Angular S.H.M. , it must be Oscillatory. Also, It must be Periodic. It cannot be simple Harmonic Motion, because simple Harmonic Motion does not involves Rotational Analogy
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