Time period and frequency of angular SHM(Simple Harmonic Motion)

Time period and frequency of angular SHM

When a body is allowed to rotate freely about a given axis then the oscillation is known as the angular oscillation. 

The point at which the resultant torque acting on the body is taken to be zero is called mean position. If the body is displaced from the mean position, then the resultant torque acts such that it is proportional to the angular displacement and this torque has a tendency to bring the body towards the mean position.

Let  be the angular displacement of the  body and the resultant torque  the body is

κ is the restoring torsion constant, which is  torque per unit angular displacement. If I is  the moment of inertia of the body and  is the angular acceleration then

This differential equation resembles simple harmonic differential equation.

So, comparing equation (10.17) with simple harmonic motion given in equation (10.10), we have

The frequency of the angular harmonic motion (from equation 10.13) is