Follow the steps indicated here to derive the equation of motion of a pendulum, equation

Chapter 1, Problem 22

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Follow the steps indicated here to derive the equation of motion of a pendulum, equation (12) in the text. Assume that the rod is rigid and weightless, that the mass is a point mass, and that there is no friction or drag anywhere in the system. a. Assume that the mass is in an arbitrary displaced position, indicated by the angle . Draw a free-body diagram showing the forces acting on the mass. b. Apply Newtons law of motion in the direction tangential to the circular arc on which the mass moves. Then the tensile force in the rod does not enter the equation. Observe that you need to find the component of the gravitational force in the tangential direction. Observe also that the linear acceleration, as opposed to the angular acceleration, is Ld2/dt2, where L is the length of the rod. c. Simplify the result from part b to obtain equation (12) in the text.