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  • Topic: Pendulum, Pendulum clock, Pendulums
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This article is about pendulums. For the band, see Pendulum (band). For other uses, see Pendulum (disambiguation). "Simple gravity pendulum" assumes no air resistance and no friction.| An animation of a pendulum showing the velocity and acceleration vectors (v and A).| | A pendulum is a weight suspended from a pivot so that it can swing freely.[1] When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. A pendulum swings with a specific period which depends (mainly) on its length. From its discovery around 1602 by Galileo Galilei the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s.[2] Pendulums are used to regulate pendulum clocks, and are used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geophysical surveys, and even as a standard of length. The word 'pendulum' is new Latin, from the Latin pendulus, meaning 'hanging'.[3] The simple gravity pendulum[4] is an idealized mathematical model of a pendulum.[5] [6] [7] This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. When given an initial push, it will swing back and forth at a constant amplitude. Real pendulums are subject to friction and air drag, so the amplitude of their swings declines. Contents[hide] * 1 Period of oscillation * 2 Compound pendulum * 3 History * 3.1 1602: Galileo's research * 3.2 1656: The pendulum clock * 3.3 1673: Huygens' Horologium Oscillatorium * 3.4 1721: Temperature compensated pendulums * 3.5 1851:Foucault pendulum * 3.6 1930: Decline in use * 4 Use for time measurement * 4.1 Clock pendulums * 4.2 Temperature compensation * 4.2.1 Mercury pendulum * 4.2.2 Gridiron pendulum * 4.2.3 Invar and fused quartz * 4.3 Atmospheric pressure * 4.4 Gravity * 5 Accuracy of pendulums as timekeepers * 5.1 Q factor * 5.2 Escapement * 5.3 The Airy condition * 6 Gravity measurement * 6.1 The seconds pendulum * 6.2 Early observations * 6.3 Kater's pendulum * 6.4 Later pendulum gravimeters * 7 Standard of length * 7.1 Early proposals * 7.2 The metre * 7.3 Britain and Denmark * 8 Other uses * 8.1 Seismometers * 8.2 Schuler tuning * 8.3 Coupled pendulums * 8.4 Religious practice * 8.5 Execution * 9 See also * 10 External links * 11 Further reading * 12 References| [edit] Period of oscillation

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,...
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