Question

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

Answer 1

The oscillating body is said to be in exactly SHM, when the restoring force of body is directly proportional to displacement covered by body.

F directly proportional to displacement

Let the displacement be x

So,

F is directly proportional to x

F = - kx ______ (1) ( k is force constant)

By second law of Newton ,

F = ma

- kx = ma

a = (-k/m)x

It shows that

a directly proportional to x

Hope it will help you