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Simple Harmonic Motion - Springs

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

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, $F = - k x$ $F=-kx$ where, $k$ $k$ is a constant

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

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

$F = - K x$ $F=-Kx$

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

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

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

Ashley H · 1 · Aug 11 2018
What is simple harmonic motion?

Answer:

This a motion where the acceleration is is directly proportional to the displacement and this acceleration is directed to a fixed point.

Explanation:

simple harmonic motion(SHM) is isochronous. this means the period of the oscillations is independent of the amplitude. this hold true when the oscillation is undamped .

Geh · 1 · Jun 14 2018

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