A Level Physics Notes: Waves and Oscillations – The Simple Pendulum
Resolving at P for the pendulum:
Towards F:
(1)
Applying
along
the tangent of the arc PO:
(2)
The minus sign indicates the acceleration is in the direction of
decreasing
Equation
(1) we can ignore since the motion is along the arc of the circle and
this equation is derived by resolving perpendicular to the motion.
We consider equation (2). If
is
small then
(2) becomes
The length of a circular arc is
and
the acceleration of the pendulum above is
(3)
If we make the substitution
then
the above equation (3) becomes
which
has the form of the simple harmonic motion equation.