Expression for Period in SHM

The angular velocity of the body moving in a circle is

When the body completes one revolution, q = 360^o or 2p radians and the time taken by the body is called the period T. In this time, the body executing SHM will have completed one oscillation and therefore T is also the period of SHM.

Multiplying equation

by m , the mass of the particle

According to Newton's 2ⁿ^d law of motion

But for a particle in SHM,

F = -Ky according to equation - - - - (1)

Substituting for w in equation (2.48), we get

Sub Topics

Thus, the period in SHM depends on two factors

Thus, the period in SHM depends on two factors

The mass of the oscillating particle

The force constant of the spring (or any other agency) which supplies the restoring force.

The above equation tells us that period is independent of the amplitude. Such a motion is said to be isochronous.