1/2 (')^2 + a/2 (')^2 - cos = I + C where C is the constant of integration. The term 1/2 (')^2 is the kinetic energy (since ' is the velocity), and -cos is the potential energy. The term a/2 (')^2 represents energy loss due to damping, and I represents work done by the external driving current. So, the energy of the system is: E = 1/2 (')^2 - cos