What is the relationship between amplitude and period of a pendulum?
The period of swing of a simple gravity pendulum depends on its length, the acceleration of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, θ, called the amplitude. It is independent of the mass of the bob. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is: T = 2 x pi x sqrt (L /g) where L is the length of the pendulum and g is the local acceleration of gravity.
