# Simple Pendulum 1 .pdf - QATAR UNIVERSITY Mathematics for...

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QATAR UNIVERSITYMathematics for EngineeringMath 217-L51Dr. Houssein AyoubSimple PendulumAlhanof AlNaemiFatima Alsulaiti
Page | 1AbstractSimple pendulum or other types of pendulum have played a key role in many advancements inthe domain of physics, time measurement, climate and earthquake predictions and many otherapplications.One of the first clocks that could show time will relative accuracy were all dependent on apendulum continuous movement. The period of the oscillation was the main factor on which theclock worked and it was adjusted in manner that a complete period was of 1sec.The understanding of the motion of a simple pendulum is important as it gives insight tounderstanding of objects motion under gravity, the inertial change in a body during its motionand the effect of centripetal and external forces on the motion of a body. Thus, a completeanalysis of a simple pendulum motion gives a complete analysis of a simple harmonic motionwith forces in balance.
Page | 2Table of ContentsAbstract............................................................................................................................................1Table of Figures...............................................................................................................................2Introduction.....................................................................................................................................3Derivations and Results...................................................................................................................4Conclusion.......................................................................................................................................9Bibliography....................................................................................................................................9Authors’ Contributions....................................................................................................................9Table of FiguresFigure 1- Simple Pendulum (NAgle, 2012).....................................................................................3
Page | 3IntroductionA simple pendulum is can be taken as a suspended mass attached to a spring or rod whose masscan be neglected. The mass resonant at a fix frequency until the motion of the pendulum diesdown and it comes back to its original form. An illustration of a pendulum is shown below:Figure 1- Simple Pendulum (NAgle, 2012)The period of oscillation of the pendulum depends on the length of the string and the mass ofthe suspended mass. The mass is resolved into its component and by using the newton’s secondlaw of torque equals to the rate of change of angular momentum a second order nonlineardifferential equation is derived. The nonlinear terms in the equation due to the component ofthe mass along the direction of the motion. The main objective is to find an expression for thetime period of the pendulum using differential equations technique.

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Term
Spring
Professor
NoProfessor
Tags
Jacobi s elliptic functions, Jacobi Elliptic