Post by bluefedish on Dec 22, 2007 20:33:09 GMT -5
A pendulum is an object that is attached to a pivot point so it can swing freely. This object is subject to a restoring force that will accelerate it toward an equilibrium position. When the pendulum is displaced from its place of rest, the restoring force will cause the pendulum to oscillate about the equilibrium position. In other words, a weight attached to a string swings back and forth.
A basic example is the simple gravity pendulum or bob pendulum. This 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.
The regular motion of pendulums can be used for time keeping, and pendulums are used to regulate pendulum clocks.
History
As recorded in the 20th century Chinese Book of Later Han, one of the earliest uses of the pendulum was in the seismometer device of the Han Dynasty scientist and inventor Zhang Heng. Its function was to sway and activate a series of levers after being disturbed by the tremor of an earthquake far away. After this was triggered, a small ball would fall out of the urn-shaped device into a metal toad's mouth below, signifying the cardinal direction of where the earthquake was located (and where government aid and assistance should be swiftly sent).
An Egyptian scholar, Ibn Yunus, is known to have described an early pendulum in the 10th century. Some claimed that he used it for making measurements of time, but this is now believed to be a misinterpretation on the part of Edward Bernard, an English historian.
Among his scientific studies, Galileo Galilei performed a number of observations of all the properties of pendulums. His interest in pendulums may have been sparked by looking at the swinging motion of a chandelier in the Pisa cathedral. He began serious studies of the pendulum around 1602. Galileo noticed that period of the pendulum is independent of the bob mass or the amplitude of the swing. He also found a direct relationship between the square of the period and the length of the arm. The isochronism of the pendulum suggested a practical application for use as a metronome to aid musical students, and possibly for use in a clock.
Perhaps based upon the ideas of Galileo, in 1656 the Dutch scientist Christiaan Huygens patented a mechanical clock that employed a pendulum to regulate the movement. This approached proved much more accurate than previous time pieces, such as the hourglass. Following an illness, in 1665 Huygens made a curious observation about pendulum clocks. Two such clocks had been placed on his mantlepiece, and he noted that they had acquired an opposing motion. That is, they were beating in unison but in the opposite direction—an anti-phase motion. Regardless of how the two clocks were adjusted, he found that they would eventually return to this state, thus making the first recorded observation of a coupled oscillator.
During his Académie des Sciences expedition to Cayenne, French Guiana in 1671, Jean Richer demonstrated that the periodicity of a pendulum was slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne. Huygens reasoned that the centripetal force of the Earth's rotation modified the weight of the pendulum bob based on the latitude of the observer.
In his 1673 opus Horologium Oscillatorium sive de motu pendulorum, Christian Huygens published his theory of the pendulum. He demonstrated that for an object to descend down a curve under gravity in the same time interval, regardless of the starting point, it must follow a cycloid (rather than the circular arc of a pendulum). This confirmed the earlier observation by Marin Mersenne that the period of a pendulum does vary with amplitude, and that Galileo's observation was accurate only for small swings in the neighborhood of the center line.
The English scientist Robert Hooke devised the conical pendulum, consisting of a pendulum that is free to swing in both directions. By analyzing the circular movements of the pendulum bob, he used it to analyze the orbital motions of the planets. Hooke would suggest to Isaac Newton in 1679 that the components of orbital motion consisted of inertial motion along a tangent direction plus an attractive motion in the radial direction. Isaac Newton was able to translate this idea into a mathematical form that described the movements of the planets with a central force that obeyed an inverse square law—Newton's law of universal gravitation. Robert Hooke was also responsible for suggesting (as early as 1666) that the pendulum could be used to measure the force of gravity.
In 1851, Jean-Bernard-Leon Foucault suspended a pendulum (later named the Foucault pendulum) from the dome of the Panthéon in Paris. The mass of the pendulum was 28 kg and the length of the arm was 67 m. Once the pendulum was set in motion, the plane of motion was observed to precess 360° clockwise once per day. To Foucault, the precession was most easily explained by the rotation of the Earth.
The National Institute of Standards and Technology based the U.S. national time standard on the Riefler Clock from 1904 until 1929. This pendulum clock maintained an accuracy of a few hundredths of a second per day. It was briefly replaced by the double-pendulum W. H. Shortt Clock before the NIST switched to an electronic time-keeping system.
Some Uses
* Spiritual Healing - in the body, causes or solutions, etc.
* Inner Growth
* To Locate Things - water, gold, oil and other minerals; lost objects; vacation spots; underground pipes and leaks; faulty equipment and sources of malfunctions, etc.
* To Determine - compatibility between people, places and things; health of plants and animals; counterfeit or authentic items; honesty or fairness, etc.
* To Choose - investments and stocks; careers; relationships; dates; timing; healthful foods, etc.
Selected Sources:
en.wikipedia.org/wiki/Pendulum
www.pendulums.com/practical_uses.htm
A basic example is the simple gravity pendulum or bob pendulum. This 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.
The regular motion of pendulums can be used for time keeping, and pendulums are used to regulate pendulum clocks.
History
As recorded in the 20th century Chinese Book of Later Han, one of the earliest uses of the pendulum was in the seismometer device of the Han Dynasty scientist and inventor Zhang Heng. Its function was to sway and activate a series of levers after being disturbed by the tremor of an earthquake far away. After this was triggered, a small ball would fall out of the urn-shaped device into a metal toad's mouth below, signifying the cardinal direction of where the earthquake was located (and where government aid and assistance should be swiftly sent).
An Egyptian scholar, Ibn Yunus, is known to have described an early pendulum in the 10th century. Some claimed that he used it for making measurements of time, but this is now believed to be a misinterpretation on the part of Edward Bernard, an English historian.
Among his scientific studies, Galileo Galilei performed a number of observations of all the properties of pendulums. His interest in pendulums may have been sparked by looking at the swinging motion of a chandelier in the Pisa cathedral. He began serious studies of the pendulum around 1602. Galileo noticed that period of the pendulum is independent of the bob mass or the amplitude of the swing. He also found a direct relationship between the square of the period and the length of the arm. The isochronism of the pendulum suggested a practical application for use as a metronome to aid musical students, and possibly for use in a clock.
Perhaps based upon the ideas of Galileo, in 1656 the Dutch scientist Christiaan Huygens patented a mechanical clock that employed a pendulum to regulate the movement. This approached proved much more accurate than previous time pieces, such as the hourglass. Following an illness, in 1665 Huygens made a curious observation about pendulum clocks. Two such clocks had been placed on his mantlepiece, and he noted that they had acquired an opposing motion. That is, they were beating in unison but in the opposite direction—an anti-phase motion. Regardless of how the two clocks were adjusted, he found that they would eventually return to this state, thus making the first recorded observation of a coupled oscillator.
During his Académie des Sciences expedition to Cayenne, French Guiana in 1671, Jean Richer demonstrated that the periodicity of a pendulum was slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne. Huygens reasoned that the centripetal force of the Earth's rotation modified the weight of the pendulum bob based on the latitude of the observer.
In his 1673 opus Horologium Oscillatorium sive de motu pendulorum, Christian Huygens published his theory of the pendulum. He demonstrated that for an object to descend down a curve under gravity in the same time interval, regardless of the starting point, it must follow a cycloid (rather than the circular arc of a pendulum). This confirmed the earlier observation by Marin Mersenne that the period of a pendulum does vary with amplitude, and that Galileo's observation was accurate only for small swings in the neighborhood of the center line.
The English scientist Robert Hooke devised the conical pendulum, consisting of a pendulum that is free to swing in both directions. By analyzing the circular movements of the pendulum bob, he used it to analyze the orbital motions of the planets. Hooke would suggest to Isaac Newton in 1679 that the components of orbital motion consisted of inertial motion along a tangent direction plus an attractive motion in the radial direction. Isaac Newton was able to translate this idea into a mathematical form that described the movements of the planets with a central force that obeyed an inverse square law—Newton's law of universal gravitation. Robert Hooke was also responsible for suggesting (as early as 1666) that the pendulum could be used to measure the force of gravity.
In 1851, Jean-Bernard-Leon Foucault suspended a pendulum (later named the Foucault pendulum) from the dome of the Panthéon in Paris. The mass of the pendulum was 28 kg and the length of the arm was 67 m. Once the pendulum was set in motion, the plane of motion was observed to precess 360° clockwise once per day. To Foucault, the precession was most easily explained by the rotation of the Earth.
The National Institute of Standards and Technology based the U.S. national time standard on the Riefler Clock from 1904 until 1929. This pendulum clock maintained an accuracy of a few hundredths of a second per day. It was briefly replaced by the double-pendulum W. H. Shortt Clock before the NIST switched to an electronic time-keeping system.
Some Uses
* Spiritual Healing - in the body, causes or solutions, etc.
* Inner Growth
* To Locate Things - water, gold, oil and other minerals; lost objects; vacation spots; underground pipes and leaks; faulty equipment and sources of malfunctions, etc.
* To Determine - compatibility between people, places and things; health of plants and animals; counterfeit or authentic items; honesty or fairness, etc.
* To Choose - investments and stocks; careers; relationships; dates; timing; healthful foods, etc.
Selected Sources:
en.wikipedia.org/wiki/Pendulum
www.pendulums.com/practical_uses.htm
