Determination of periodic solutions in systems with a straight-line characteristic composed of line pieces parallel to the two given straight lines

The determination of periodic solutions in systems with a nonlinear characteristic composed of two straight-line pieces is considered. Periodic solutions of corresponding differential equations are found in the form of complete Fourie series without neglecting harmonics.
The solution of the problem is reduced to determination of the equation of periods. The knowledge of the equation roots permits to form the desired periodic solutions using the known formulae.
The method for the determination of the equation of periods suggested in the paper does not require to solve systems of linear equations describing the process along the certain intervals.