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

##### 1 Answer

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,

Here,

In case of spring,if we compress it by

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,

Now,you can compare it with equation of S.H.M i.e

So,here,

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