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).

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.

tp = 2П

or

tp=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/tp Hertz