Show that in simple harmoni motion, the acceleration is directly proportional to its displacement at the given instant.

Explanation

Consider the instantaneous displacement of particle executing SHM,
`y=A sin (omega-phi)`
The instantaneous velocity of the particle `v=(dy)/(dt)=omega A cos (omega t-phi)`
The instantaneous acceleration of the particle `=a=(dv)/(dt)`
i.e., `a=-omega^(2)A sin (omegat-phi)`
`i.e., a=-omega^(2)y`
Hence `a prop y` and acts opposite to the displacement.