Explain what is phase and draw in a single graph of different phases of simple harmonic motions.

Solution :The position of a particle is determined by the equation `x(t)= A cos (omega t+PHI)` in time t. Where `(omega t+ phi)` is called PHASE of the motion or phase in the time t. It shows the position of motion of OSCILLATOR at that time.
Phase-constant (Phase angle) : ..At time to t=0, the phase of simple harmonic oscillator is known initial phase or phase-constant or phse angle...
If the amplitude is fixed, then at time t=0, initial phase `phi` can be determine from displacement of particle.
`x(t) = A cos phi ""[therefore t=0]`
`therefore cos phi = (x(t))/(A)`
`therefore phi = cos^(-1) ((x(t))/(A))`
The curves 3 and 4 are for `phi = 0" and "phi = -(PI)/(4)` respectively. The amplitude A is samefor both the PLOTS as shwon in figure.