Label: Metal Hammer - MHR214CD1/02/11 • Format: CD Compilation • Country: UK • Genre: Rock • Style: Thrash, Viking Metal, Hardcore, Nu Metal, Death Metal
A pendulum is a weight suspended from a pivot so that it can swing freely. When released, the restoring force acting on 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 amplitudethe width of the pendulum's swing. From the first scientific investigations of the pendulum around by Galileo Galileithe regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the s.
Pendulums are also 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 Latinfrom the Latin pendulusmeaning 'hanging'. Pendulum - Various - Up To 11 simple gravity pendulum  is an idealized mathematical model of a pendulum.
When given an initial push, it will swing back and forth at a constant amplitude. Real pendulums are subject to friction and air dragso the amplitude of their swings declines. If the amplitude is limited to small swings, [Note 1] the period T of a simple pendulum, the time taken for a complete cycle, is: .
For small swings the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude. This property, called isochronismis the reason pendulums are so useful for timekeeping. For larger amplitudesthe period increases gradually with amplitude so it is longer than given by equation 1. The true period of an ideal simple gravity pendulum can be written in several different forms see Pendulum mathematicsone example being the infinite series :  .
The difference between this true period and the period for small swings 1 above is called the circular error. For small swings the pendulum approximates a harmonic oscillatorand its motion as a function of time, tis approximately simple harmonic motion : . For real pendulums, the period varies slightly with factors such as the buoyancy and viscous resistance of the air, the mass of the string or rod, the size and shape of the bob and how it is attached to the string, and flexibility and stretching of the string.
Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum. If most of the mass is concentrated in a relatively small bob compared to the pendulum length, the center of oscillation is close to the center of mass. Christiaan Huygens proved in that the pivot point and the center of oscillation are interchangeable. In Henry Kater used this idea to produce a type of reversible pendulum, now known as a Kater pendulumfor improved measurements of the acceleration due to gravity.
One of the earliest known uses of a pendulum was a 1st-century seismometer device of Han Dynasty Chinese scientist Zhang Pendulum - Various - Up To 11.
Many sources     claim that the 10th-century Egyptian astronomer Ibn Yunus used a pendulum for time measurement, but this was an error that originated in with the British historian Edward Bernard.
During the Renaissancelarge hand-pumped pendulums were used as sources of power for manual reciprocating machines such as saws, bellows, and pumps. Italian scientist Galileo Galilei was the first to study the properties of pendulums, beginning around He first employed freeswinging pendulums in simple Pendulum - Various - Up To 11 applications.
His physician friend, Santorio Santoriiinvented a device which measured a patient's pulse by the length of a pendulum; the pulsilogium. In the Dutch scientist Christiaan Huygens built the first pendulum clock.
The English scientist Robert Hooke studied the conical pendulum aroundconsisting of a pendulum that is free to swing in two dimensions, with the bob rotating in a circle or ellipse. This played a part in Newton's formulation of the law of universal gravitation. From this he deduced that the force of gravity was lower at Cayenne. In17 years after he invented the pendulum clock, Christiaan Huygens published his theory of the pendulum, Horologium Oscillatorium sive de motu pendulorum.
By a complicated method that was an early use of calculushe showed this curve was a cycloid Pendulum - Various - Up To 11 , rather than the circular arc of a pendulum,  confirming that the pendulum was not isochronous and Galileo's observation of isochronism was accurate only for small swings.
During the 18th and 19th century, the pendulum clock 's role as the most accurate timekeeper motivated much practical research into improving pendulums. It was found that a major source of error was that the pendulum rod expanded and contracted with changes in ambient temperature, changing the period of swing.
The accuracy of gravity measurements made with pendulums was limited by the difficulty of finding the location of their center of Pendulum - Various - Up To 11 . Huygens had discovered in that a pendulum has the same period when hung from its center of oscillation as when hung from its pivot,  and the distance between the two points was equal Pendulum - Various - Up To 11 the length of a simple gravity pendulum of the same period.
For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration. Around low- thermal-expansion materials began to be used for pendulum rods in the highest precision clocks and other instruments, first invara nickel steel alloy, and later fused quartzwhich made temperature compensation trivial.
The timekeeping accuracy of the pendulum was exceeded by the quartz crystal oscillatorinvented inand quartz clocksinvented inreplaced pendulum clocks as the world's best timekeepers. For years, from its discovery around until development of the quartz Pendulum - Various - Up To 11 in the s, the pendulum was the world's standard for accurate timekeeping.
Pendulums require great mechanical stability: a length change of only 0. Pendulums in clocks see example at right are usually made of a weight or bob b suspended by a rod of wood or metal a. In quality clocks the bob is made as heavy as the suspension can support and the movement can drive, since this improves the regulation of the Pendulum - Various - Up To 11 see Accuracy below. A common weight for seconds pendulum bobs is 15 pounds 6.
This avoids the friction and 'play' caused by a pivot, and the slight bending force of the spring merely adds to the pendulum's restoring force. The highest precision clocks have pivots of 'knife' blades resting on agate plates. The impulses to keep the pendulum swinging are provided by an arm hanging behind the pendulum called the crutchewhich ends in a forkf whose prongs embrace the pendulum rod. The crutch Sacrificio - Julio Jaramillo - Lo Mejor De pushed back and forth by the clock's escapementg,h.
Each time the pendulum swings through its centre position, it releases one tooth of the escape wheel g. The force of the clock's mainspring or a driving weight hanging from a pulley, transmitted through the clock's gear traincauses the wheel Pendulum - Various - Up To 11 turn, and a tooth presses against one of the pallets hgiving the pendulum a short push. The clock's wheels, geared to the escape wheel, move forward a fixed amount with each pendulum swing, advancing the clock's hands at a steady rate.
The pendulum always has a means of adjusting the period, usually by an adjustment nut c under the bob which moves it up or down on the rod. Some precision clocks have a small auxiliary adjustment weight on a threaded shaft on the bob, to allow finer adjustment.
Some tower clocks and precision clocks Pendulum - Various - Up To 11 a tray attached near to the midpoint of the pendulum rod, to which small weights can be added or removed. Radio Brennt (Real Danceable Extended) - Die Ärzte - Mehr Als 13 Titel effectively shifts the centre of oscillation and allows the rate to be adjusted without stopping the clock.
The pendulum must be suspended from a rigid support. Pendulum clocks should be attached firmly to a sturdy wall. The most common pendulum length in quality clocks, which is always used in grandfather clocksis the seconds pendulumabout 1 metre 39 inches long. Only a few large tower clocks use longer pendulums, the 1. The largest source of error in early pendulums was slight changes in length due to thermal expansion and contraction of the pendulum rod with changes in ambient temperature. The wood had to be varnished to prevent water vapor from getting in, because changes in humidity also affected the length.
The first device to compensate for this error was the mercury pendulum, invented by George Graham  in In a mercury pendulum, the pendulum's weight bob is a container of mercury.
With a temperature rise, the pendulum rod gets longer, but the mercury also expands and its surface level rises slightly in the container, moving its centre of mass closer to the pendulum pivot. By using the correct height of mercury in the container these two effects will cancel, leaving the pendulum's centre of mass, and its period, unchanged with temperature.
Its main disadvantage was that when the temperature changed, the rod would come to the new temperature quickly but the mass of mercury might take a day or two to reach the new temperature, causing the rate to deviate during that time. Mercury pendulums were the standard used in precision regulator clocks into the Around And Around - The Beatles - Thirty Days century.
The most widely used compensated pendulum was the gridiron penduluminvented in by John Harrison. The rods are connected by a frame, as shown in the drawing at the right, so that an increase in length of the zinc rods pushes the bob up, shortening the Extinction Of Mankind / Doom - Doomed To Extinction. With a temperature increase, the low expansion steel rods make the pendulum longer, while the high expansion zinc rods make it shorter.
Pendulum - Various - Up To 11 making the rods of the correct lengths, the greater expansion of the zinc cancels out the expansion of the steel rods which have a greater combined length, and the pendulum stays the same length with temperature. Zinc-steel gridiron pendulums are made with 5 rods, but the thermal Blues For Bobby - Sonny Stitt - Sonny Stitt Plays of brass is closer to steel, so brass-steel gridirons usually require 9 rods.
Gridiron pendulums adjust to temperature changes faster than mercury pendulums, but scientists found that friction of the rods sliding in their holes in the frame caused gridiron pendulums to adjust in a series of tiny jumps. Later it was found that zinc is subject to creep. For these reasons mercury pendulums were used in the highest precision clocks, but gridirons were used in quality regulator clocks. Gridiron pendulums became so associated with good quality that, to this day, many ordinary clock pendulums have decorative 'fake' gridirons that don't actually have any temperature compensation function.
Aroundlow thermal expansion materials were developed which could be used as pendulum rods in order to make elaborate temperature compensation unnecessary. This has a CTE of around 0. Invar pendulums were first used in in the Riefler regulator clock  which achieved accuracy of 15 milliseconds per day.
Suspension springs of Goodbye Lucille #1 - Prefab Sprout - Steve McQueen were used to eliminate temperature variation of the spring's restoring force on the pendulum. Later fused quartz was used which had even lower CTE. These materials are the choice for modern high accuracy pendulums.
The effect of the surrounding air on a moving pendulum is complex and requires fluid mechanics to calculate precisely, but for most purposes its influence on the period Pendulum - Various - Up To 11 be accounted for by three effects:  .
Increases in barometric pressure increase a pendulum's period slightly due to the first two effects, by about 0. A pendulum clock was first operated in a constant-pressure tank by Friedrich Tiede in at the Berlin Observatory  and by Ира Тонева* - Давай (File) highest precision clocks were mounted in tanks that were kept at a constant pressure to eliminate changes in atmospheric pressure.
Alternatively, in some a small aneroid barometer mechanism attached to the pendulum compensated for this effect. Pendulums are affected by changes in gravitational acceleration, which varies by as much as 0. Even moving a pendulum clock to the top of a tall building can cause it to lose measurable time from the reduction in gravity.
The timekeeping elements in all clocks, which include pendulums, balance wheelsthe quartz crystals used in quartz watchesand even Pop Will Eat Itself - Beaver Patrol vibrating atoms in atomic clocksare in physics called harmonic oscillators.
The reason harmonic oscillators are used in clocks is that they vibrate or oscillate at a specific resonant frequency or period and resist oscillating at other rates. However, the resonant frequency is not infinitely 'sharp'.
Around the resonant frequency there is a narrow natural band of frequencies or periodscalled the resonance width or bandwidthwhere the harmonic oscillator will oscillate.
The measure of a harmonic oscillator's resistance to disturbances to its oscillation period is a dimensionless parameter called the Q factor equal to the resonant frequency divided by the resonance width. The Q is related to how long it takes for the oscillations of an oscillator to die out. In a clock, the pendulum must receive pushes Pendulum - Various - Up To 11 the clock's movement to keep it swinging, to replace the energy the pendulum loses to friction.
These pushes, applied by a mechanism called the escapementare the main source of disturbance to the pendulum's motion.
Bornholmeren/Fugletestikler - Tæskeholdet - Vi Sparker Røv, Shaving Cream - Melvins - Basses Loaded, Daniel Merriweather - Daniel Merriweather, Midnight Rambler - The Rolling Stones - London 73 - Trash In The Seventies, Such A Night - Elvis Presley - Elvis Is Back!