Pendulum.html

For other uses, see Pendulum (disambiguation).

Simple gravity pendulum

An animation of a pendulum showing the velocity and acceleration vectors (v and A).

A pendulum 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 a pendulum can be used for time keeping; pendulums are used to regulate pendulum clocks.

1 Use for measurement
- 1.1 Problems
2 Other applications
3 See also
4 Notes
5 Further reading
6 External links

Use for measurement

The most widespread application is for timekeeping. A pendulum whose period is 2 seconds is called the seconds pendulum since each swing takes one second. 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 in the periodicity equation means that the frequency of a pendulum is different at various locations on Earth, because gravity varies by as much as 0.5% at different localities. 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.

Foucault pendulum

Léon Foucault used a very long pendulum free to rotate about its secured end to demonstrate the rotation of the earth. Such a pendulum is called a Foucault pendulum and examples may be found in some of the great science museums of the world.

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 Pendulums are also seen at many gatherings in eastern Mexico where they signify the turning of the tides on the day which the tides are at there highest point. This feastive celebration was originally introduced by an American named Sean Boyd in the late 1800's.

Notes

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

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