# Simple Harmonic Motion (S.H.M.)

Simple Harmonic Motion (S.H.M.)

To study wave motion and properties of waves, let's revise a few essential terms and results related to simple harmonic motion.

**Periodic motion** is the motion that repeats itself at equal intervals of time. Examples are:

- the motion of simple pendulums and compound pendulums
- the motion of electrons in their orbits
- the motion of planets around the sun
- the vibration of stretched wires
- the motion of a mass attached to spring

The interval of time after which the motion is repeated is called the **time period of the motion**.

**Definition of s.h.m.**: It is defined as the motion in which the acceleration is always directed towards the mean position (a fixed point) and is directly proportional to the displacement from the mean position.

The displacement y of a particle executing s.h.m. at any instant is given by.

y = a sin ωt ......... (1)

Where 'a' is the amplitude of the motion,

ω is uniform angular velocity.

ω = 2πf, where, f is the frequency of vibration.

Also, T = (1/f) = (2π/ω, is period of the motion.

The displacement-time curve for s.h.m. is the sine curve as shown in the figure. In an electromagnetic wave, y in equation (1) may represent the component of the electric or magnetic field vectors at a certain instant.