## Simple Harmonic Motion (SHM):

Simple Harmonic Motion (SHM) is the simplest form of oscillation. Suppose, a particle is executing linear periodic motion along the x-axis and the point O, which is the origin (x=0). It is the position of equilibrium of the particle.

Let D be any point on the path of the particle with position coordinate x. According to conditions, if F is the restoring force acting on the particle at D, then

F ∝ x

__Characteristics of SHM:__

1. Simple harmonic motion is a kind of linear periodic motion. In this motion, the particle moves to and from following the same path repeatedly at regular time intervals.

ii. The acceleration of the particle executing SHM is always directed toward the position of equilibrium.

iii. The acceleration of the particle is proportional to its displacement from the position of equilibrium at any instant.

iv. When the particle passes the position of equilibrium, its velocity becomes maximum. The velocity of the particle gradually reduces and momentarily comes to zero at the extremities of its path.

v. The time period of SHM doesn’t depend on the amplitude. Though the amplitude decreases gradually due to various external resistances, the time period remains unchanged.

**Note:** All simple harmonic motions are periodic, but all periodic motions are not simple harmonic.