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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 q is a small angle sinq = q 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 w²=g/l and, again, the time period can be calculated using T = 2p/w.
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© David Hoult 2008 |
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