Abstract: According to Newton＇s law of motion, we establish a couple of inhomogeneous differential equations for vibration of motion with two degrees of freedom in rotating coordinate system. The roots of equation by transforming them into the sum between the roots of a couple of homogeneous and the roots of a couple of linear equation in two unknowns are obtained. By analyzing the eigenvalues of equations, we conclude three laws of motion and get the formula of the vibration of system.

Key words: rotating coordinate system, vibration system of two degree of freedom, inhomogeneous differential equations