Definitions, equations and graphs 

            Definition of Simple Harmonic Motion (SHM):           LO (d)

A motion where the  acceleration a of an object is always directed towards a fixed point ( the equilibrium position O ) and proportional to its displacement x from the fixed point is said to be  be simple harmonic. 

        Defining equation of SHM

a =  - ω2 x

Observe from the model or the animation, suggest the reason for the negative sign.

The negative sign means a is always directed towards the equilibrium point while x is pointing away from equilibrium point O.

In other words a and x are in the opposite direction.