# Simple harmonic motion

Consider a particle *P* moving on the circumference of a circle in clockwise direction with constant angular velocity (ω). Let *N* be the projection of the point *P* on the diameter of the circle. It can be noticed that when the point *P* moves from X to *Y* then the point N moves from X to *O*. When particle P moves from Y to then N moves from O to . When P moves from to then N moves from to O and when the particle P moves from to X then N moves from O to X. In this way point P completes one revolution and point N completes one vibration. The up and down motion of point N is called Simple Harmonic motion (SHM).

The following terms are generally used in SHM.

** Amplitude:** It is the maximum displacement from the mean position. OX or is the amplitude of particle P.

** Periodic time**: Time taken by the particle P to complete one revolution.

t_{p} = 2П/ω

or

t_{p}=2П(Displacement/Acceleration)^{1/2 } Seconds

** Frequency**: It is the number of cycles per second. It is the reciprocal of time period. Units of frequency is hertz.

Frequency = f = 1/time period = 1/t_{p }Hertz