is mean position always at t = 0

In simple harmonic motion, position of particle need not be at mean position at t = 0

 

If the particle starts from mean position at t = 0, initial velocity is to be given , i.e., it starts with

given initial kinetic energy and this energy is utilized to maintain oscillation

 

Starting position can be the maximum displacement location on either side of mean position at t = 0 .

In this case stored energy is utilized to maintain the oscillations