Pendulum

A simple gravity pendulum or bob pendulum is a weight (or bob) on the end of a massless string, which, when given an initial push, will swing back and forth under the influence of gravity over its central (lowest) point.

History

The pendulum was discovered during the 10th century by Ibn Yunus, 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 by Galileo.

Basic principles

If and only if the pendulum swings through a small angle (so <math>\sin(\theta)</math> can be approximated as <math>\theta</math>) the motion may be approximated as simple harmonic motion. The period of a pendulum is significantly affected only by its length and the acceleration of gravity. The period of motion is independent of the mass of the bob or the angle at which the string hangs at the moment of release. 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

<math>T = 2\pi \sqrt\frac{\ell}{g}\,</math>

where <math>\ell</math> 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)

Applications

Timekeeping

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.

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 = 9.915 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 gravity at any point on the surface of the Earth - this is known as gravimetry.

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.

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.

Coupled pendula

Two coupled pendula form a double pendulum. Many physical systems can be mathematically described as coupled pendula. Under certain conditions these systems can also demonstrate chaotic motion.

Pendula for entertainment

A pendulum is often part of a children's playground. The swing is a type of parametric oscillator. Pendula are often part of rides found at amusement parks.

Pendula in 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 pendula for divination and dowsing.

Other Uses: Pendulums are also used for wrecking balls.

See also

• Pendulum clock
• Simple harmonic motion
• Foucault pendulum
• Spherical pendulum
• Double pendulum
• Kater's pendulum
• Harmonograph
• Metronome
• Seconds pendulum

Notes

1. ^ An interesting simulation of thurible motion can be found at this site.

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.

Wikipedia information about Pendulum This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Pendulum". It may not have been reviewed by professional editors (see full disclaimer). Help contribute to Americola and edit this article.