Question

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

Answer 1

We know that the oscillating particle is said to be in execute SHM if the restoring force oan particle is directly proportional to the displacement.

Let the displacement be x

F directly proportional to x

Then,

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

By Newton second law

F = ma

By first equation

-kx = ma

a = (- k/m) x

It shows that

a is directly proportional to x


Hope this answer will help you

Answer 2

We know that the oscillating particle is said to be in execute SHM if the restoring force on particle is directly proportional to the displacement.

Let the displacement be x

F directly proportional to x

Then,

F = - kx                   (1) ( k is an constant)

By Newtons second law

F = ma

from equation (1)

-kx = ma

a = (- k/m) x

It shows that

a is directly proportional to x