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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pendulum ： ウィキペディア英語版 Pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways 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. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing. From its examination in 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. 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'. The ''simple gravity pendulum''〔defined by Christiaan Huygens: , Part 4, Definition 3, translated July 2007 by Ian Bruce〕 is an idealized mathematical model of a pendulum. 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. == Period of oscillation == (詳細は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.〔, p.188-194〕 It is independent of the mass of the bob. If the amplitude is limited to small swings,〔A "small" swing is one in which the angle θ is small enough that sin(θ) can be approximated by θ when θ is measured in radians〕 the period ''T'' of a simple pendulum, the time taken for a complete cycle, is: :$T\; \backslash approx\; 2\backslash pi\; \backslash sqrt\backslash frac\; \backslash qquad\; \backslash qquad\; \backslash qquad\; \backslash theta\_0\; \backslash ll\; 1\; \backslash qquad\; (1)\backslash ,$ 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. Successive swings of the pendulum, even if changing in amplitude, take the same amount of time. For larger amplitudes, the period increases gradually with amplitude so it is longer than given by equation (1). For example, at an amplitude of ''θ0'' = 23° it is 1% larger than given by (1). The period increases asymptotically (to infinity) as ''θ0'' approaches 180°, because the value ''θ0'' = 180° is an unstable equilibrium point for the pendulum. The true period of an ideal simple gravity pendulum can be written in several different forms (see Pendulum (mathematics) ), one example being the infinite series:〔 includes a derivation〕 :$$ T = 2\pi \sqrt \left( 1+ \frac\theta_0^2 + \frac\theta_0^4 + \cdots \right) The difference between this true period and the period for small swings (1) above is called the ''circular error''. In the case of a typical grandfather clock whose pendulum has a swing of 6° and thus an amplitude of 3° (0.05 radians), the difference between the true period and the small angle approximation (1) amounts to about 15 seconds per day. For small swings the pendulum approximates a harmonic oscillator, and its motion as a function of time, t, is approximately simple harmonic motion:〔 :$\backslash theta\; (t)\; =\; \backslash theta\_0\; \backslash cos\; \backslash left(\; \backslash frac\backslash ,\; t\; +\backslash varphi\; \backslash right)\backslash ,$ where $\backslash varphi$ is a constant value, dependent on initial conditions. For real pendulums, corrections to the period may be needed to take into account the buoyancy and viscous resistance of the air, the mass of the string or rod, the size and shape of the bob and how it is attached to the string, flexibility and stretching of the string, and motion of the support.〔〔J. S. Deschaine and B. H. Suits, "The hanging cord with a real tip mass," European Journal of Physics, Vol 29 (2008) 1211–1222.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pendulum」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.