The mathematical model of the forced synchronization system, composed of four oscillators is investigated. The mathematical model of the system is the matrix differential equation with delayed arguments. The matrix differential equation is solved using method of steps and applying Laplace transform. Using this method and exact solution of the matrix differential equation with delayed arguments was obtained and exact expressions of the elements of the step responses matrix, of the synchronization system are got. On the base of derived formulas the transition processes of the system are investigated.