This report is the second in series investigating the feasibility of supplementing base isolation with active bang-bang control mechanisms. We formulate discrete approximations to energy- and power-balance equations for a base isolated structure supplemented with constant stiffness bang-bang (CKBB) control. Numerical experiments are conducted to: (1) Identify situations when constant stiffness bang-bang control is most likely to add value' to system responses due to base isolation alone, and (2) Quantitatively determine the work done and power required by the actuators. A key observation from the numerical experiments is that overall performance' of the actuators is coupled to ``input energy per unit time.'