Question

show that in SHM the acceleration is directly proportional to its displacement at the given instant of time. can anyone please tell it in simple words

Answer 1

Simple harmonic motion is charcterized by a restoring force that varies linearly with position. This allows us to write (for the sake of simplicity, I'm going to do this in one dimension)F=−bxF=−bx where the negative sign indicates that it is a restoring force, bb is a proportionality constant, and xx is the displacement from the equilibrium position. If the restoring force is the only force acting in the system, then we can write Fnet=ma=−bxFnet=ma=−bx. So we get: a=−bmxa=−bmx

If we let −bm=c−bm=c then we get a=cxa=cx which shows us that the acceleration is directly proportional to the displacement.