Quantitative Analysis of SHM

Let us consider a particle executing Simple Harmonic Motion between A and A₁ about passing through the mean position (or) equilibrium position (O). Its analysis is as follows

SHM about Position O

Displacement	x = -A	x = 0	x = +A
Acceleration	|a| = Max	a = 0	|a| = max
Speed	|v| = 0	|v| = Max	|v| = 0
Kinetic energy	KE = 0	KE = Max	KE = 0
Potential energy	PE = Max	PE = Min	PE = Max

Equation of Position of a Particle as a Function of Time

Let us consider a particle, which is executing SHM at time t = 0, the particle is at a distance from the equilibrium position.

Necessary conditions for Simple Harmonic Motion