9.2 Simple Harmonic Motion (S.H.M)
The motion of a body to and fro about a fixed point is called Simple Harmonic Motion. The motion is periodic (which repeats itself after equal interval of time) and its acceleration is always directed towards the mean position and is proportional to its distance from the mean position. The motion of a simple pendulum (as shown in the figure) is S.H.M.
Let a body executing S.H.M. is represented by the equations
where x and represents the displacement, velocity and acceleration of the body respectively.
SINUSOIDAL MOTION
This is periodic vibratory motion and is referred as Simple Harmonic motion. It can be
shown mathematically as
