A body moving along a circular path is acted upon the centripetal acceleration given byThis is directed towards the centre of the circle. The component of this acceleration parallel to the vertical diameter, represents the acceleration of the particle executing SHM. This component is ac sinq, as seen in figure. It is in the downward direction. It is opposed to the displacement, which is upward. To represent this opposition, a negative sign is attached.
Conclusion: A particle in simple harmonic motion has zero acceleration at the mean position and maximum acceleration at the extreme position.
The graph of acceleration versus the phase angle is a negative sine curve which is shown in the figure below.
We find from the graphs in figure, that the velocity is 90o out of phase with the displacement, while the acceleration is 180o out of phase with the displacement.
