In this paper, the electromagnetic and mechanical characteristics of the improved homopolar linear synchronous motor (H-LSM) have been studied. Firstly, the influence of the ratio of the width and pitch of the rotor teeth is investigated on the magnetic field distribution and vibration traits. By establishing a simplified three-dimensional magnetic circuit model, the distribution of air gap flux density is attained. Secondly, the time and space distributions of the air gap flux density is decomposed, and the ratio of tooth width to tooth pitch with larger fundamental component is selected as the key index to design the H-LSM. Thirdly, through the modal analysis of the primary core, detailed investigation on the harmonics response is carried out, and the resonance frequency domain in the working process is clarified. Finally, 1-10th order frequency spectrum on the H-LSAM resonance is decomposed, which can provide a judgment for the fault diagnosis.