Innovative optimal charging sequences are sought to minimize battery degradation and reduce charging loses. One charging sequence under investigation incorporates high frequency pulses or sinusoidal perturbations. However, there is disagreement in the literature on the benefits/disadvantages of pulsed charging. This work analytically determines optimal battery charging sequences for two cases: minimizing energy losses and maximizing charge supplied to the battery while respecting lithium plating constraints. Assuming relevant battery physics have linear, time-invariant dynamic behavior, optimal charging strategies are derived analytically. The analysis exposes specific features of the battery dynamic response (frequency response and impulse response) that must be present for optimal charging sequences to have periodic components. In the case of energy minimization, the battery's electrochemical impedance must approach the imaginary axis. In the case of limiting lithium plating, a criterion is developed involving impulse responses of relevant battery variables.