The motion of a simple pendulum is approximately SHM only if the amplitude is small. Consider a

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The motion of a simple pendulum is approximately SHM only if the amplitude is small. Consider a simple pendulum that is released from a horizontal position (θi = 90° in Fig. 10.23).

(a) Using conservation of energy, find the speed of the pendulum bob at the bottom of its swing. Express your answer in terms of the mass m and the length L of the pendulum. Do not assume SHM. 

(b) Assuming (incorrectly, for such a large amplitude) that the motion is SHM, determine the maximum speed of the pendulum. Based on your answers, is the period of a pendulum for large amplitudes larger or smaller than that given by Eq. (10-41)?


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