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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.
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Use for measurement
The most widespread application is for timekeeping. A pendulum whose time period is 2 seconds is called the seconds pendulum since most clock escapements move the seconds hands on each swing. Clocks that keep time with the use of pendulums lose accuracy due to friction. Pendulums are also widely used as metronomes for musicians.
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/s2) is transported to Cairo, Egypt, (g = 9.793 17 m/s2) 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.
Problems
Pendulums in air are affected by atmospheric and mechanical drag. These effects can be compensated for if they are known and constant. Atmospheric drag is affected by the density of air, which is in turn affected by its moisture content, temperature, and barometric pressure. Precise clocks used for the timing of astronomic observations were improved by operating the pendulum in a partially evacuated and temperature controlled chamber. Since the drag is proportional to the square of the velocity, a long pendulum or a pendulum with a high rotational moment of inertia about its pivot, which both produce slow oscillation, will be less affected by atmospheric drag than is a faster pendulum.
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.
Other applications
Schuler tuning
As first explained by Maximilian Schuler in his classic 1923 paper, a pendulum whose period exactly equals the orbital period of a hypothetical satellite orbiting just above the surface of the earth (about 84 minutes) will tend to remain pointing at the center of the earth when its support is suddenly displaced. This is the basic principle of Schuler tuning that must be included in the design of any inertial guidance system that will be operated near the earth, such as in ships and aircraft. Pendulums are used in swing metronomes for pianists.
Religious practice
Pendulum motion appears in religious ceremonies as well. The swinging incense burner called a censer, also known as a thurible, is an example of a pendulum.[1]
See also
Notes
Further reading
- 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.
External links
- 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
Wikipedia content modification information:
- This page was last modified on 11 October 2008, at 00:12.
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