Simple Pendulum
The net restoring force is
Fnet = - m g sin - m g sin = m a
a = - g sin
And this is not exactly what we had for our prototype,
Fnet = - 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!
(c) 2005, Doug Davis; all rights reserved
Vertical Spring Torsional Pendulum Return to ToC, Oscillations