Abstract: The dynamical equations for a two-gimbal dynamically tuned gyroscope with mass unbalance in both the rotor and the gimbals are put forward as a development based on ideal suspension.The effects of linear acceleration on gyro's drift have been analyzed. The main results can be summarized as follows:1.Although the mass center of the rotor and the gimbals does not coincide with the suspension center, the drift effect due to the twice spin frequency angular vibration may be eliminated by proper selection and adjustment of the principal moments of inertia of the gimbals.2.If the vehicle possesses the constant linear accelerations about the axes normal to the driving shaft, the erratic disturbing torques acting on the rotor will emerge.3.If the vehicle possesses the linear acceleration of twice spin frequency about axes normal to the driving shaft, the erratic disturbing torques acting on the rotor will emerge.4.If the vehicle possesses the linear acceleration of the same spin frequency in the direction of the driving shaft, the erratic disturbing torques acting on the rotor also will emerge.5.The formulae for gyro's drift under the effect of all kinds of spin frequency linear vibration inputs are given in the last table.A theoretical basis for the mathematical model of gyro's erratic compensation is established for engineering purpose,