In order to improve the stability of the micromechanical gyroscope, the dynamic performance of the L-L type two-mass micromechanical gyroscope on the movable base in free vibration state is studied, and the mathematical model of the micromechanical gyroscope is established to obtain the solution of the motion differential equation with amplitude-phase as the variable, and the relation between the solution and the orbital elements is given. In addition, the effects of the frame mass and the nonlinear stiffness of elastic parts on the gyro drift are studied, and a numerical example is given. Finally, the obtained analytic relation and curve are analyzed, and the corresponding conclusions about the system performance are drawn.