Im supposed to calculate the work done by the frictional force on a simple pendulum after one period. I have to use the following equation to do this calculation. ((beta)^2)'= (2g/l)(cosbeta - costheta) where thetha is the the maximum angle of the motion. In other words theta is the angle at which the derivative of beta=0. l is the length of the pendulum string. How do I use this equation to determine the path taken by the pendulum so I know what I am integrating the force of friction over? By the way, I am given information regarding the initial position of the ball above the floor, the length of the pendulum wire, and the ceiling height.