Consider the problem of a simple pendulum. The system consists of a bob of mass m attached to one end of a rod of length l and the other end is pivoted to a fixed point O, as shown in Fig...

Consider the problem of a simple pendulum. The system consists of a bob of mass m attached to one end of a rod of length l and the other end is pivoted to a fixed point O, as shown in Fig. 1.2.1(a). Assume that: (1) the bob as well as the rod connecting the bob to the fixed point O are rigid, (2) the mass of the rod is negligible relative to the mass of the bob that is constant, and (3) there is no friction at the pivot. Derive the differential equation governing the periodic motion of the simple pendulum and determine the analytical solution to the small-amplitude motion (i.e. linear solution) of the bob.