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 = ma

a = - ( k / m ) x

Or is it?

Look more closely at this sin :

sin = opp / hyp

sin = opp / hyp

sin = x / l

And for small angles, this is nearly equal to

sin = 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 is a SHO for small angular displacements!

Vertical Spring			Torsional Pendulum
Return to ToC, Periodic Motion

(c) 2002, Doug Davis; all rights reserved