The Simple Pendulum

The restoring force, F, is a component of the force of gravity acting on the bob.

Therefore the magnitude of F is given by

but, it is clear that, if x is positive, F acts in the negative sense and when x is negative, F acts in the positive sense therefore we must write

This force produces an acceleration, a, given by

However, if is a small angle sin = in radians and so we have

a = -g =

So, the motion is s.h.m. (for small angles) and the constant relating acceleration to displacement is given by and, again, the time period can be calculated using .

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