In this research, an analytical solution of the dynamic excitation of elastic system depending on parametric changes in the stiffness of teeth during engagement is presented. It is shown that the main source of excitation in a differential gear is the central internal gear, and the intensity of the excitation depends on the manufacturing accuracy of the tooth profile. With increase of the flank size on the addendum of the sun gear more than a particular value, vibration levels in the gear increases. Introduction of optimal value of pitch variation in gear wheel reduces vibration to minimum.