Pendulum (mathematics)

The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small-angle oscillations.

Simple gravity pendulum

A so-called "simple pendulum" is an idealization of a "real pendulum" but in an isolated system using the following assumptions:

The differential equation which represents the motion of a simple pendulum is

where g is acceleration due to gravity, ℓ is the length of the pendulum, and θ is the angular displacement.

Small-angle approximation

The differential equation given above is not easily solved, and there is no solution that can be written in terms of elementary functions. However adding a restriction to the size of the oscillation's amplitude gives a form whose solution can be easily obtained. If it is assumed that the angle is much less than 1 radian, or

! (disambiguation)

! is a punctuation mark called an exclamation mark (33 in ASCII), exclamation point, ecphoneme, or bang.

! may also refer to:

Mathematics and computers

Music

Other

See also

The Servant (band)

The Servant was an English alternative band, formed in London in 1998. They are popular in France, Spain, Switzerland as well as other European countries.

Their first introduction to an American audience was in the trailer of the film Sin City with the instrumental version of their song "Cells". This version of "Cells" is not on the Sin City soundtrack, but it can be downloaded via their website ("Cells" was also used in the film The Transporter and Transporter 2, along with their song, "Body"). Since the Sin City trailers, there has been significant U.S. interest in their records and demands for live concerts. The band released their fourth album entitled How To Destroy A Relationship in 2006.

Before achieving commercial success in 2004 with their self-titled album, released by Prolifica Records in the UK and by Recall Group in France, The Servant released two EP's: Mathematics in 1999 and With the Invisible in 2000.

On 26 November 2007, the band announced on their blog at MySpace that they were splitting up "to move on to pastures new".

Mathematics (producer)

Mathematics, also known as Allah Mathematics, (born: Ronald Maurice Bean) is a hip hop producer and DJ for the Wu-Tang Clan and its solo and affiliate projects.

Biography

Born and raised in Jamaica, Queens, New York, Mathematics was introduced to hip hop by his brother who used to bring home recordings of the genre's pioneers like Grandmaster Flash & The Furious Five, Treacherous Three and Cold Crush Brothers. He began his career in 1987 DJing block parties and park jams in Baisley Projects, going by the name Supreme Cut Master. In 1988, he became the full-time DJ for experienced rapper Victor C, doing countless shows in clubs and colleges in New York City.

In 1990, Mathematics linked up with GZA/Genius; he soon became one of the Wu-Tang Clan's founding members, but at the time GZA was struggling to build a career on the Cold Chillin' label. This partnership earned Mathematics a spot on his first official tour, The Cold Chillin Blizzard Tour (with popular acts such as Biz Markie, Big Daddy Kane, Kool G. Rap & DJ Polo and Marley Marl).

Pendulum

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing.

From its examination in around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s. Pendulums are used to regulate pendulum clocks, and are used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geophysical surveys, and even as a standard of length. The word "pendulum" is new Latin, from the Latin pendulus, meaning 'hanging'.

Pendulum (disambiguation)

A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity.

Pendulum may also refer to:

In music:

Pendulum (EP)

Pendulum is the debut EP from Brisbane musician Tara Simmons.

It features the single "Everybody Loves You" which received airplay on Triple J and a nomination in the Q Song Awards in 2006. "Everybody Loves You" and "Break The Rules For Me" were both featured in the independent film All My Friends Are Leaving Brisbane. Only the former was included on the soundtrack album.

Track listing