THE SIMPLE PENDULUM
ITS PERIOD OF OSCILLATION
TO MEASURE G= 9.807 MS-2
AND AS A CLOCK

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Contents

1. INTRODUCTION
 PENDULUM
 HISTORY OF PENDULUM

 MAIN BODY
 EXPERIMENTAL PROCEDURE
 GRAPH OF T AGAINST L
 PLOTTING OF TWO DIFFERENT VARIABLES
 COUNTING OF GRAVITATIONAL ACCELERATION
 SIMPLE PENDULUM AS A DEVICE
 TO MEASURE TIME

2. FURTHER EXPLORATION

3. CONCLUSION

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Introduction

Pendulum

A pendulum is a mass that is attached to a pivot, from which it can swing freely. This object is subject to a restoring force due to gravity 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.
A basic example is the simple gravity pendulum or bob pendulum. This is a mass (or bob) on the end of a massless string, which, when initially displaced, will swing back and forth under the influence of gravity over its central (lowest) point.
The regular motion of the pendulum can be used for time keeping, and pendulums are used to regulate pendulum clocks.
History of Pendulum
As recorded in the 5th century Chinese Book of Later Han, one of the earliest uses of the pendulum was in the seismometer device of the Han Dynasty (202 BC - 220 AD) scientist and inventor Zhang Heng (78-139). 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.

Galileo Galilei
Among his scientific studies, Galileo Galilei performed a number of observations of all the properties of pendulums. His interest in the pendulum 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 discovered the key property that makes pendulums useful timekeepers: isochronism, which means that the period of the pendulum is approximately independent of the amplitude (width) of its swing, so that successive swings of the pendulum will take the same amount of time even if the swing is decreasing due to friction. He also found that the period of a pendulum is independent of the mass of its bob, and proportional to the square root of its length. 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 approach 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 fireplace mantel, 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 work Horologium Oscillatorium sive de motu pendulorum, Christiaan Huygens published his theory of the pendulum. He demonstrated that for an object to descend a curve under gravity in the same time interval, regardless of the starting point, it must follow a cycloid curve, rather than the circular arc that a pendulum follows. This confirmed the earlier observation by Marin Mersenne that the period of a pendulum does vary with amplitude, and that Galileo's observation of isochronism 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. It was the third Foucault pendulum he constructed, the first one was constructed in his basement and the second one was a demonstration model with a length of 11 meters. The mass of the pendulum in Pantheon was 28 kg and the length of the arm was 67 m. The Foucault pendulum was a worldwide sensation: it was the first demonstration of the Earth's rotation with a purely indoors experiment. Once the Paris pendulum was set in motion the plane of motion was observed to precess about 270° clockwise per day. A pendulum located at either of the poles will precess 360° per day relative to the ground it is suspended above. There is a mathematical relation between the latitude where a Foucault pendulum is deployed and its rate of precession; the period of the precession is inversely proportional to the sine of the latitude.
For 270 years, from their invention until quartz crystal oscillators superseded them in the 1920s, pendulums were the world's most accurate timekeeping technology. The most accurate pendulum clocks, called astronomical regulators, were installed in astronomical observatories, and served as standards to set all other clocks. The National Institute of Standards and Technology based the U.S. national time standard on the Riefler clock made by the German firm Clemens Riefler, 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 quartz clocks in the 1930s.

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Procedure

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Conclusion

My data showed the period of my simple pendulum to be independent of mass, which is consistent with the uncertainty of the measurements made with the stopwatch.

Time is measured to the nearest 0.01s but I might expect the vagueness of the measurements to be slightly larger than that since the stopwatch itself is somewhat inadequate and there is some small variation in the reaction time of the experimenter which is me.

My value of G was within 5.935% of the theoretical value, but again the range of the experimental values obtained for G does not quite take account of the expected experimental value. These differences are small and can probably be explained by some of the small errors listed above, which were not necessarily accounted for in the uncertainty calculations. Hence my result seem to be in agreement with existing theory, but in order to determine this for certain, I would need to do further investigation, attempting to control some of these variables.





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