This paper focuses on comparing the effects of varying degrees of electromechanical coupling in piezoelectric power harvesting systems on the dynamics of charging a storage capacitor. In order to gain an understanding of the behavior of these dynamics, a transducer whose vibrational dynamics are impacted very little by electrical energy extraction is compared to a transducer that displays strong electromechanical coupling. Both transducers are cantilevered piezoelectric beams undergoing base excitation whose harvested electrical energy is used to charge a storage capacitor. The transient dynamics of the coupled system are studied in detail with an emphasis on their charging power curves and the time to charge the storage capacitor to a specified voltage. An analytic model for the system is derived that takes into consideration the reduction in vibration amplitude of the beam caused by the removal of electrical energy. Although this model makes the typical assumption that the beam is vibrating at its open-circuit resonance, it is shown to predict the charging behavior of the system accurately when compared to experimental results and a complete, nonlinear simulation without this simplification. Finally, the simplifications and discrepancies created by several types of modeling assumptions for a highly coupled energy harvesting system are discussed.