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pendulum, a mass, called a bob, suspended from a fixed point so that it can swing in an arc determined by its momentum and the force of gravity. The length of a pendulum is the distance from the point of suspension to the center of gravity of the bob (see center of mass). Chance observation of a swinging church lamp led Galileo to find that a pendulum made every swing in the same time, independent of the size of the arc. He used this discovery in measuring time in his astronomical studies. His experiments showed that the longer the pendulum, the longer is the time of its swing. Christiaan Huygens determined an exact relation between the length of the pendulum and the time of vibration when the arc of swing is small. He arrived at the formula *T* = 2πl/g, where *T* is the period, or time for one complete swing, *l* is the length, *g* is the acceleration of gravity (see gravitation), and π = 3.14 … (see harmonic motion). In 1673, Huygens devised a practicable means of making a pendulum control the speed with which a clock mechanism runs. This impetus to clockmaking resulted not only in the development of many types of clock, such as the "wag at the wall," the grandfather clock, and the banjo clock, but also in the application of pendulum control to other mechanisms. Metal pendulums are lengthened by heat; to counteract the effect of temperature changes, compensation pendulums have been devised, many of them operating by the opposite expansion of different metals in compound rods. Forces acting on the bob, such as air resistance, affect its swing. Since gravity varies from place to place, the pendulum has been used to determine the shape and mass of the earth by measuring the intensity of gravity. In the seismograph (see seismology), a pendulum registers the direction of an earthquake. In 1851, J. B. L. Foucault demonstrated the rotation of the earth by suspending in the Panthéon in Paris a 200-ft (61-m) pendulum that traced its path in sand on the floor. The pendulum continued to vibrate in a single plane as the earth rotated underneath it, thus leaving a series of traces in the sand in all directions. A pendulum made to swing in a circle, describing a cone, is called a conical pendulum. In the torsion pendulum the bob vibrates by twisting and untwisting, as in the balance wheel of a watch.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

A pendulum is a mass that is attached to a pivot, from which it can swing freely. This object is subject to a restoring force due to gravity that will accelerate it toward an equilibrium position. When the pendulum is displaced from its place of rest, the restoring force will cause the pendulum to oscillate about the equilibrium position.

A basic example is the simple gravity pendulum or bob pendulum. This is a mass (or bob) on the end of a string of negligible mass, which, when initially displaced, will swing back and forth under the influence of gravity over its central (lowest) point.

The regular motion of the pendulum can be used for time keeping, and pendulums are used to regulate pendulum clocks.

The presence of g as a variable in the periodicity equation for a pendulum means that the frequency is different at various locations on Earth. So, for example, when an accurate pendulum clock in Glasgow, Scotland, (g = 9.815 63 m/s^{2}) is transported to Cairo, Egypt, (g = 9.793 17 m/s^{2}) the pendulum must be shortened by 0.23% to compensate. The pendulum can therefore be used in gravimetry to measure the local gravity at any point on the surface of the Earth. Note that g = 9.8 m/s² is a safe standard for acceleration due to gravity if locational accuracy is not a concern.

A pendulum in which the rod is not vertical but almost horizontal was used in early seismometers for measuring earth tremors. The bob of the pendulum does not move when its mounting does and the difference in the movements is recorded on a drum chart.

Simple pendulums in everyday clocks are affected by the ambient temperature, which thermal expansion of the material holding the bob will change the period of the pendulum. This change of length can be minimized by using special materials for the pendulum rod which exhibit little change with temperature or by using a more complex gridiron pendulum, sometimes called a "banjo" pendulum for its similarity in appearance to the musical instrument.

- Michael R.Matthews, Arthur Stinner, Colin F. Gauld. The Pendulum: Scientific, Historical, Philosophical and Educational Perspectives. Springer, 2005.
- Michael R. Matthews, Colin Gauld and Arthur Stinner. The Pendulum: Its Place in Science, Culture and Pedagogy. Science & Education, 2005, 13, 261-277.
- Morton, W. Scott and Charlton M. Lewis (2005). China: Its History and Culture. New York: McGraw-Hill, Inc.
- Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd.

- Graphical derivation of the time period for a simple pendulum
- Time period of a pendulum of infinite length
- A more general explanation of pendulum methods
- Web-based calculator of pendulum properties from numerical inputs
- Simple Pendulum Applet

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Last updated on Friday October 10, 2008 at 17:12:22 PDT (GMT -0700)

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