Purpose. The purpose of the article is to establish the basic laws of operation of induction-type linear electromechanical converter (LEMС) during operation in high-speed and shock-power modes and excitation from an AC source of increased frequency. Methodology. With the help of a mathematical model, the regularities of the course of processes in a LEMС, excited from an AC source, were established when working with shock-power and high-speed modes. The solutions of the equations of the mathematical model, which describe interrelated electrical, magnetic, mechanical and thermal processes, are presented in a recurrent form. Results. It was found that when the LEMC operates in the shock-power mode, the maximum value of the current in the inductor winding occurs in the first half-period, and in the inhibited armature winding in the second half-period. The electrodynamic force changes at twice the frequency, taking on both positive and negative values. Since the positive values exceed the negative ones, the magnitude of the impulse of the electrodynamic force increases with each period of the force. Depending on the initial voltage phase, the relative change in the magnitude of the force impulse is 1.5 %. It was found that when the LEMC operates in high-speed mode, the current in the inductor winding in the first half-period has the greatest value, but after several periods it takes on a steady state. The temperature rise of the inductor winding increases with the time of connection to the AC source, and the temperature rise of the armature winding has the nature of saturation. The electrodynamic force has an oscillatory character with strong damping and a significant predominance of the positive component. Depending on the initial phase of the voltage, the relative change in the maximum speed of the armature winding is 2.5 %. Originality. For the first time, a mathematical model of the LEMC, excited from an AC source, was developed, the solutions of the equations of which describe the interrelated electrical, magnetic, mechanical and thermal processes. For the first time, the regularities of the course of processes in LEMC were established when working with shock-power and high-speed modes. Practical value. The characteristics of LEMC are obtained, which determine the efficiency of work in shock-power and high-speed modes. It is shown that the initial voltage phase has no significant effect on the power, high-speed thermal performance of the converter excited from an alternating current source.