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5.41.} An object that swings hack and forth is called a physical pendulum. A simple pendulum is a special case of the physical pendulum and consists of a rod of length L with a mass m attached at one end [see the gure below}. If the motion of a simple pendulum takes place in a vertical plane and it is assumed that the mass of the rod is negligible and no damping forces act on the system, then it can be shown that the displacement angle B of the pendulum as a function of time I, measured from the vertical, is given by 15' Mt) = Ho cos rot + sh: mt. Here 6., and 110 are the initial displacement and velocity and or = E, and g = 32 ftfsz is the acceleration due to gravity. [3] Find 6(t) if an :> D and on = I] at t = D. {b} Show that the period {in seconds} of motion of a simple pendulum is T = 211E