This paper is devoted to a study of dynamics of an L-L-type two-mass micromechanical gyroscope (abbreviated as MMG) under forced oscillations. The mechanical-theoretical model of MMG with a sensitive element in the form of a model with two active masses (“Inertial mass -Frame”) is obtained. Based on the model, the system of differential equations is written. A distinctive feature of this paper is that an arbitrary angular velocity of the base Ω is considered. A new method is used to find a solution to the system. This method is suitable for analyzing dualfrequency systems. Finally, the solution is determined, and the amplitude-frequency characteristics of the system are described. The obtained analytical expressions and graphs are analyzed, and the reasonable conclusions about system behavior under forced oscillations are made. The proposed method for analyzing complex systems is compared with other available methods.