Problem $6)(4$ points$)$ The equation of motion of a simple pendulum is given by

ml$2$ $=$mglsin $$ kl$2$ $+$ T$,$

where l denotes the length of the rod, m denotes the mass of the bob, is the angle subtended by the rod

and the vertical axis through the pivot point, and g is the acceleration due to the gravity, k is the positive

friction coefficient, and T is the torque applied at the pivot point.