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Mechanics
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
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 .

