Compund Pendulum Essay

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OBJECT: To study the properties of a compound pendulum, and to determine the acceleration due to gravity by the use of such a pendulum. METHOD: An experimental pendulum is suspended successively about several axes at different points along its length and the period about each axis is observed. A graph is plotted of the period versus the distance of the axis of suspension from one end of the pendulum. The nature of the graph shows the physical properties of the compound pendulum. From values of the period and the corresponding length of the equivalent simple pendulum as determined from the graph, the acceleration due to gravity is calculated. From the mass of the pendulum and its radius of gyration as obtained from the curve, the rotational inertia of the pendulum is computed. THEORY: A simple pendulum consists of a small body called a “bob” (usually a sphere) attached to the end of a string the length of which is great compared with the dimensions of the bob and the mass of which is negligible in comparison with that of the bob. Under these conditions the mass of the bob may be regarded as concentrated at its center of gravity, and the length l of the pendulum is the distance of this point from the axis of suspension. When a simple pendulum swings through a small arc, it executes linear simple harmonic motion of period T, given by the equation T = 2π √(l/g) (1) where g is the acceleration due to gravity. This relation-ship affords one of the simplest and most satisfactory methods of determining g experimentally. When the dimensions of the suspended body are not negligible in comparison with the distance from the axis of suspension to the center of gravity, the pendulum is called a compound, or physical, pendulum. Any body mounted upon a horizontal axis so as to vibrate under the force of gravity is a compound pendulum. The motion of such a body is an angular

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