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A pendulum is an item hanging from a rigid position so as to move freely back and forth under the action of gravity (Bossel, 2007, p. 109). Its standard motion has worked as the foundation for measurement as documented by Galileo. This research seeks to establish the contribution or impact of the length of the swing on the periods of the pendulum and establish a mathematical association between the period and the length. This experiment tests the hypothesis that only length of the swing affects the periods of the pendulum. In view of the fact that the length of the swing, which the mass is suspended on, is reduced, the scale of the period for the pendulum gets greater than before. This experiment attempted to make a replica of Galileo's findings on these key points and validate his claims. Therefore, Galileo's procedures had to be tailored in more than a few ways to be realistic for resources of this experiment. For this experiment a five feet wide wooden swing was suggested. The experiment also used an eleven years old boy as additional mass to the mass of the swing. In this experiment various factors were tested. First and foremost, the effects of angle were tested to establish whether or not they had an impact on the periods of the pendulum. Secondly, the effects of mass on the periods of the pendulum were also tested. More so, this report came to a conclusion that the periods of the pendulum were only affected by the length of the swing. Neither the mass nor the angle of the swing affects the period of the pendulum.

The pendulum was chosen to redeem myself after miscounting the periods of the pendulum during lab and costing me and lab partner valuable points. Besides redemption, I was interested in how such a basic everyday phenomenon could be observed and analyzed by a person and turn into the basis for many modern day physics applications. The pendulum’s discovery by Galileo changed the quality of human life immeasurably. Many of the things we use and enjoy every day started with the discovery of the pendulum including: musical rhythm due to the metronome, pulse checking devices and accurate timekeeping. The physics behind the pendulum or oscillations, such as, the conservation of energy and inertia contained within Newton’s first and second laws of motion also helped in the development of some modern devices such as cell phones, watches, and bifilar pendulums (earthquake detectors). The simple swing of an object reveals the key to gravity, motion and energy.

Background

A pendulum is an item hanging from a rigid position so as to move freely back and forth under the action of gravity. A mass m suspended from a swing with a length is L and a point on which this weight is fixed describes a simple pendulum (Serway & Jewett, 2009, p. 459). It was developed by a number of physicists, mainly by Galileo in the 17^{th} century. Its standard motion has worked as the foundation for measurement, as documented by Galileo. Huygens used the notion to clock mechanisms. Additional applications entail the application by NASA to determine the material property of space flight payloads and seismic instrumentation. The fundamental equation is at the core of numerous problems concerning structural dynamics. Structural dynamics trades with the calculation of a structure’s vibratory movements. Instances comprise the bounciness or smoothness of the vehicle one rides in, the movement that one can observe if you look through the window of an aircraft in a bouncy flight, the collapse of buildings and roads in a quake and everything else that bounces, vibrates or crashes. With this pendulum movement as a point of reference, compound structures can be studied.

The pendulum functions as a figure of Newton’s 2^{nd} Law, which affirms that for each force there is an equivalent and opposite feedback. The basic experiments demonstrate another of Newton’s laws, that is, bodies in motion continue to move unless acted on by another force. The pendulum offers a widespread collection of experiments that can be carried out using inexpensive and materials that are easy to obtain. The measurements necessitate no particular skills and apparatus.

When the mass suspended from the swing is dispatched with a preliminary angle, it begins to move about with a periodic motion. The movement can be estimated as a straightforward harmonic movement if the pendulum swings all the way through a small angle. Therefore, the period and frequency for the straightforward pendulum are independent of the preliminary angle of the movement. In addition, the period does not depend on the weight of the swing. Nevertheless, it is impacted by the length of the swing, which the weight is suspended on and the gravity acceleration.

In this experiment, the period of a home-based pendulum was measured. The objective of this experiment was to find out which variables influence the movement of a pendulum. The main aim of this experiment wasto establish the contribution or impact of the length of the swing on the period for the pendulum and form a mathematical association between the period and the length.

This experiment also tested the hypothesis that only length of the swing affects the periods of the pendulum. In view of the fact that the length of the swing, which the mass is suspended on, is reduced, the scale of the period for the pendulum gets greater than before. Dissimilar masses of the item suspended from the string bears no effect on the period. The controlled variables in this experiment were mass and angle. The dependent variable was the period of the pendulum.

Materials

- Huskey brand tape measure black and silver;
- 4 feet wooden level;
- 5 feet wide wooden swing;
- Stopwatch;
- Weight.

Procedure

The length of the swing was measured from the top of its chain connected at the top to the center of the base of the swing. The swing was then pulled back three steps. A distance of 35 inches was measured, and then the level was placed at that distance. Standing behind the level, the swing was released. Ten seconds were counted as the periods were also counted. The distance was then doubled back to 70 inches. The procedure was repeated. The periods were the same 3,5 periods. Then this was modified due to the low number of periods and for graphing purposes, which entailed counting to 60 seconds in which time there were 18 periods. This entire process was repeated with mass added to the swing, an 11 year old boy sitting on the swing. The results were the same with mass added: 18 periods at both 35 and 70 inches.

The pendulum swings through small displacements side to side from its rest point at an unchanging period that is reliant on the acceleration of gravity and the length of the swing. This is expressed by the equation:

T= 2π√L/G (Loyd, 2007, p. 198)

Note that the heaviness of the swing is not expressed in this equation. This indicates that despite the weight, a mass that is hanged on a specific length of swing, will take an identical time to finish a set motion, for instance, 10 cycles. The angle, which the pendulum swings through from side to side, is not indicated in the expression either. This shows that the period does not depend on the angle of swing. This is factual whether you move backward and forward the pendulum a small bit or a larger value of angle. However, for extremely large angles, a difference will be observed. This is a description of an experiment that illustrates these notions. What one can determine, and how one can present the findings and what can be calculated to substantiate the theory are described (Wilson & Hernández, 2009, p.40).

Galileo's Pendulum Experiments

Galileo made use of pendulums expansively in his studies. At the first part of his career, he studied the distinctiveness of their movement. After studying their behavior, he was capable of using them as time measurement tools in later experiments. Galileo also carried out experiments to study the nature of collisions. He made use of pendulums; however, these studies appear to have offered less information and to have been less definite than the other studies.

Time determination was a key issue in a lot of Galileo's studies. For the pendulum experiments, Galileo appears to have made a comparison of the pendulums in pairs over an identical time. For instance, an individual would be allocated to each pendulum of the pair. Each person would then determine the number of oscillations flanked by the words start and stop. This technique was utilized for assessment in these experiments (Newton, 2005, p. 50).

Galileo made an observation that the bobs of pendulums practically go back to their discharge height. In the present day, this fact illustrates the conservation of energy. This principle was not yet revealed during Galileo's time. As a pastime, pendulums were discharged from dissimilar heights. The position the pendulum went back to was distinguished and measured up to the release point. Quantitative measurements were not made, however, in each examination; the pendulum's return point was extremely close to its release point. The estimated variation between the points was no more than three mm for the range of swing lengths used.

Galileo also made an observation that pendulums with lesser weight come to rest more quickly. As a check of this study, two pendulums, almost identical apart from their bobs of dissimilar weights, were dispatched at the same height and time. The lighter bob comes to the rest faster than the heavier swing. More so, Galileo asserted to have suspended pendulums of lead and cork from his ceiling and determined their periods to be identical. This indicates that mass has effect on their periods.

Galileo asserts that the pendulum period was not dependent of the amplitude. Scholars argue whether he intended that the periods are precisely identical or that they vary to a slight degree. He further found that the period squared is relative to the length for the pendulum.

Conclusion

In conclusion, the objective of the experiment was to study the contribution or impacts of the length of the swing on the period a pendulum and realize a mathematical association between the period and the length. According to the information collected during the study, the weight of the entity suspended from the swing has no impact on the period of the pendulum. The period is dependent on the length of the swing, which the weight is hanged on. Increasing the length of the swing leads to an increase in the value of the period.

This experiment manages to test theories about pendulum as postulated by Galileo. Italian physicist and mathematician postulated that the periods of the stages were only affected by the length of the swing. This is evident from the results of the experiment. When the length of the swing is reduced, the number of periods also increased as a result. However, the number of periods did not change as a result of increase in mass on the swing. In this case, there was no change in the number of periods due to the increase of weight of the eleven year boy. Eleven years boys are fairly heavy. This means that the mass added on the swing was fairly high. Furthermore, the change in angle did not cause any change in the number of periods of the pendulum. The change in angle was effected with the change in release distance of the swing from 35 inches to 75 inches. However, a large amount of change in the angle can cause a difference in the number of periods of the pendulum.

This experiment therefore, confirmed the prediction that only the length of the swing causes an effect on the periods of the pendulum. The variables in this experiment were successfully controlled by simply adjusting the time. In addition, the change of length could be effected to make changes in this experiment. This experiment also managed to answer the question what are the effects of mass, length and angle on the periods of the pendulum. Based on these results, new question can be hypothesized, among them: what is the effect of mass on the periods of the pendulum? What is the effect of angle in the periods of the pendulum? Considering the scope of this experiment, this was a good experiment.

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