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

1 Answer
Aug 11, 2018

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.