# Pendulums

Topics: Pendulum, Pendulum clock, Pendulums Pages: 26 (10171 words) Published: April 18, 2011

Main article: Pendulum (mathematics)
The period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, θ0, called the amplitude.[8] 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:[9]

where L is the length of the pendulum and g is the local acceleration of gravity. For small swings, the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude. This property, called isochronism, is the reason pendulums are so useful for timekeeping.[10] Successive swings of the pendulum, even if changing in amplitude, take the same amount of time. This formula is strictly accurate only for tiny infinitesimal swings. For larger amplitudes, the period increases gradually with amplitude so it is longer than given by equation (1). For example,...