The differential equation for the Simple harmonic motion has the following solutions:
- x=Asinωt (This solution when the particle is in its mean position point (O) in figure (a)
- x0=Asinϕ (When the particle is at the position & (not at mean position) in figure (b)
- x=Asin(ωt+ϕ) (When the particle at Q at in figure (b) (any time t).
These solutions can be verified by substituting this x values in the above differential equation for the linear simple harmonic motion.