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Simple Pendulum Essay

1396 words - 6 pages

De La Salle University-DasmariñasCity of Dasmariñas, CavitePHYS204LSound, Waves and Optics LaboratorySarain, Camille B. July 25, 2013HUB31/Group 3 August 01, 2013Experiment No. 3Simple Harmonic Motion(The Simple Pendulum)Sir Emmanuel T. SantosProfessorAbstractSimple Harmonic motion involving a swinging pendulum was studied. The experiment focuses on the effect of the length of pendulum on period as well as the determination of the magnitude of acceleration due to gravity. As the pendulum oscillated, it's time to complete 50 vibrations was measured using a stopwatch. The results showed that period has a direct relationship with the length of the pendulum. The acceleration of gravity was computed using the slope of the plotted graph, 13.13mls2 which accumulated a 33.88% error. The sources of error were inaccurate measurement of time and the slight rotation of the pendulum during oscillation. In was concluded that when the length of a simple pendulum increases, the period of oscillation also increases. And there are only two factors that affect the period, the length of the pendulum and the acceleration due to gravity.IntroductionAnother simple device besides the spring-mass that can produce simple harmonic motion is the simple pendulum. A simple pendulum consists merely of a point-mass (m) suspended from a fixed point by a rod or string of length (L). The mass of the rod or string is assumed to be so much less than the suspended mass that it can be ignored. If the suspended mass is displaced to the left or right, while the rod or string is kept taut, and then released, the mass will swing freely back and forth under the gravity's influence. For small horizontal displacements (angular displacements of less than 10°, for instance), the restoring force on the suspended is given by:F = ma = m (- g/L) xHere, m is the mass of the point-mass or bob, g is the magnitude of the gravitational acceleration, L is the length of the string or rod, and x is the horizontal displacement. The presence of the minus sign is not a typographical error and merely says that the restoring force points in a direction opposite to the displacement. Since m, g, and L are positive constants, we note that formula (1) has the same form as the equation for Hooke's Law. Recall that Hooke's law is of the form (F = -k x). Although we won't prove it, it can be shown that an object is subject to Hooke's law, or any other force that can be expressed in a form similar to Hooke's law, it will execute simple harmonic motion. We therefore expect that the suspended mass of the simple pendulum will execute simple harmonic motion.MethodologyFig.1The simple pendulum was set up as shown in Fig. 1. The initial length of pendulum was made 120cm. The diameter of the bob was measured with vernier calliper. The length of the string was measured from the point of suspension to the top of the bob (careful not to stretch the sting as the length is measured). The radius of the bob was...

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