Pendulum
Learn more about Pendulum
- For torsion pendula, see torsion spring. For the mathematics involved with pendulums, see pendulum (mathematics). For the Drum n' Bass/Breaks band see Pendulum (band). For other uses, see pendulum (disambiguation)
A simple gravity pendulum or bob pendulum (plural pendulums or pendula), is a weight (or bob) 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 |
[edit] Basic principles
If and only if the pendulum swings through a small angle (less than 15 degrees) 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.
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).
[edit] Applications
[edit] Timekeeping
The most widespread application is for timekeeping. A pendulum whose time period is two 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.
[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] Pendulums for entertainment
A pendulum is often part of a children's playground. The swing is a type of parametric oscillator. Pendulums are often part of rides found at amusement parks.
[edit] Pendulums 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.<ref>An interesting simulation of thurible motion can be found at this site.</ref>
[edit] Notes
<references/>
[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 methodsbg:Махало
da:Matematisk pendul de:Pendel es:péndulo fa:آونگ fr:Pendule (physique) it:Pendolo ja:振り子 he:מטוטלת מתמטית ms:Bandul nl:Slinger (natuurkunde) pl:Wahadło pt:Pêndulo simples ru:Математический маятник sl:Nihalo sv:Pendel
