Abstract: Based on the Coulomb law and the Newton second law，the damping vibration dynamic equation of charged particles in four fixed points charge electric field is theoretically expressed and the analytical solution is obtained. The conditions of under-damp，critical damp and over-damp are analyzed and discussed. Finally，some example images are drawn by using MATLAB mathematical software.

Key words: charged particles, electric field of four fixed point charge, damping vibration, example images