A torsional pendulum is an oscillator for which the restoring force is torsion. For example, suspending a bar from a thin wire and winding it by an angle , a torsional torque

(1)

is produced, where is a characteristic property of the wire, known as the torsional constant. Therefore, the equation of motion is

(2)

where I is the moment of inertia. But this is just a simple harmonic oscillator with equation of motion

(3)

where is the initial angle,

(4)

is the angular frequency, and is the phase.

Pendulum, Torsional Constant, Torsional Torque