ANGULAR SIMPLE HARMONIC MOTION

When a rigid body is set free to rotate about a fixed axis and is displaced from its equilibrium orientation, it can undergo angular oscillation exactly analogous to linear SHM. The mean (equilibrium) position is the orientation at which the net restoring torque on the body is zero. If the body is twisted away from this orientation by an angular displacement $\vec\theta$, a restoring torque $\vec\tau$ develops that always tries to bring it back: $\vec\tau\propto-\vec\theta$, written $\vec\tau=-\kappa\vec\theta$, where $\kappa$ (kappa) is the restoring torsion constant -- the torque needed per unit angular displacement, a property of the particular suspension (e.g. a torsion fibre). If $I$ is the moment of inertia of the oscillating body about the axis and $\vec\alpha$ its an …