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

Show that in simple harmoni motion, the acceleration is directly propo

1.	Show that in simple harmoni motion, the acceleration is directly proportional to its displacement at the given instant.
Answer» Solution :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.