The commensurate increase of unsprung mass due to in-wheel motors can have negative effects on either ride comfort or roadholding capability of electric vehicles (EVs). To counteract those effects, semi-active or fully active suspension systems are deployed, which tend to be high-energy consumers. This is undoubtedly problematic for EVs, since battery life and range are already limiting factors in design. Furthermore, when performance is comparable, passive suspension systems are preferred due to their simplicity, higher reliability, lower implementation cost, and zero energy consumption. In this work, using an energy-based approach, we conduct the frequency analysis response of a suspension system containing a transverse third-damper. A transverse half-car model is employed, and the behaviors of both wheels are analyzed based on disturbances on one wheel. Our results show that with an optimal damping ratio for the transverse damper, the amplitude ratio at the second resonance of one wheel could be significantly decreased, especially for high ( kg) and medium ( kg) unsprung masses. The implication is that the decrease in roadholding capability and reliability of the motor bearings associated with in-wheel motors can be mitigated. Additionally, the behavior of the sprung mass with the third-damper suspension system was identical to that of the conventional system (though the analysis was strictly limited to vertical motion). Therefore, due to its passive nature, the third-damper suspension system design is a low-cost solution that may be able to achieve the goals of improving roadholding without affecting rider's comfort. Future experimental work and other types of analysis (e.g., roll dynamics) should be carried out to provide a more complete picture of third-damper suspension system behavior.