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 ((i = 90° in Fig. 10.22).
(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. (10-26b)?