The dynamic characteristics of electric drive systems are crucial in electric vehicles. Based on the dynamic finite element method and previous studies, this study proposes and analyzes a new mathematical model for a motor longitudinally mounted on a centralized electric drive system of a pure electric vehicle. First, we analyze the largest torque ripple of a fractional slot concentrated winding inner-mounted permanent magnet synchronous motor designed for commercial electric vehicles. This torque ripple is identified as one of the excitations influencing the dynamic performance of the electric drive system. Second, a new dynamic mathematical model for the electric drive system is established. Third, we investigate the linear vibration responses of the system subject to torque ripple and transmission error. Finally, the relationships between critical motor parameters and dynamic mesh force are revealed. The results demonstrate that the proposed theoretical method can effectively determine the dynamic characteristics of the electric drive system, thereby providing valuable theoretical guidance for the design and optimization of the motor and electric drive system.