## Simple Pendulum

The net restoring force is

F _{net}= - m g sin- m g sin = m a

a = - g sin

And this is not exactly what we had for our prototype,

F _{net}= - k x = maa = - ( k / m ) x

Or is it?

Look more closely at this sin :

sin = opp / hyp sin = opp / hyp

sin = x / l

And for

smallangles, this is nearly equal tosin = s / l Now we have

a = - g sin or

a = - g (s / l) or

a = - ( g / l ) s where s is the displacement from equilibrium.

So this simple pendulum

isa SHO forsmall angular displacements!(c) 2002, Doug Davis; all rights reserved

Vertical SpringTorsional PendulumReturn to ToC, Periodic Motion