Question

Explain how a simple spring is an example of simple harmonic motion?

Answer 1

Simple harmonic motion is defined as an oscillatory motion where displacement occurs against the direction of a force acting and that force is proportional to the one degree power of displacement.

That means, `F=-kx` where, `k` is a constant

Here, `F` is the force acting and `x` is the displacement.

In case of spring,if we compress it by `x` due to its elastic recoil,restoring force generated is `F=Kx` where,`K` is the spring constant!

Now,this restoring force tries to return back the original length of the spring,i.e it acts against the direction of displacement caused to it.

So,the force-displacement relationship turns out to be,

`F=-Kx`

Now,you can compare it with equation of S.H.M i.e `F=-kx`

So,here, `k=K` i.e the spring constant.

Thereby simple spring motion fulfills the required criteria of being an S.H.M.