A simple gravity pendulum or bob pendulum (plural pendulums or pendula), is a weight on the end of a rigid rod (or a string/rope), which, when given an initial push, will swing back and forth under the influence of gravity over its central (lowest) point.
The pendulum was discovered by Ibn Yunus during the 10th century, who was the first to study and document its oscillatory motion. Its value for use in clocks was introduced by physicists during the 17th century, following observations from Galileo.
Contents [hide]
1 Basic principles
2 Applications
2.1 Timekeeping
2.2 Gravimetry
2.3 Seismology
2.4 Schuler tuning
2.5 Coupled pendulums
2.6 Pendulums for divination and dowsing
3 See also
4 External links
[edit] Basic principles
The period of a pendulum is significantly affected only by its length and the acceleration of gravity.
The period of the pendulum is the time taken for two swings (left to right and back again) of the pendulum. The formula for the period, T, is
where is the length of the pendulum measured from the pivot point to the bob's center of gravity,. For a more detailed discussion of the mathematics of pendulums, see pendulum (mathematics).
[edit] Applications
[edit] Timekeeping
The most widespread application is for timekeeping. A pendulum whose time period is two seconds is called the second pendulum since most clock escapements move the seconds hands on each swing.
[edit] Gravimetry
The presence of g as a variable in the above equation means that the pendulum frequency is different at different places on Earth. So for example if you have an accurate pendulum clock in Glasgow (g = 9.815 63 m/s2) and you take it to Cairo (g = 9.793 17 m/s2), you must shorten the pendulum by 0.23%. g = 9.8 m/s² is a safe standard for acceleration due to gravity if locational accuracy is not a concern.
The pendulum can therefore be used in surveying to measure the local acceleration due to gravity at any point on the surface of the Earth - this is known as gravimetry.
[edit] Seismology
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.
[edit] 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.
[edit] Coupled pendulums
Two coupled pendulums form a double pendulum. Many physical systems can be mathematically described as coupled pendulums. Under certain conditions these systems can also demonstrate chaotic motion.
[edit] Pendulums for divination and dowsing
Pendulums (these may be a crystal suspended on a chain, or a metal weight) can also be used in divination and dowsing. See pendulums for divination and dowsing for a more detailed discussion.
[edit] See also
Pendulum clock
Simple harmonic motion
Foucault pendulum
Spherical pendulum
Double pendulum
Kater's pendulum
Harmonograph
Metronome
[edit] External links
A more general explanation of pendulums
Pendulum oscillations research by Veljko Milković
FORTRAN code for a numerical model of a simple pendulum
FORTRAN code for modeling of a simple pendulum using the Euler and Euler-Cromer methods
Retrieved from "http://en.wikipedia.org/wiki/Pendulum"
Categories: Classical mechanics | Timekeeping
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