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.

In the final dissertation you will find analyzed the two - mass electromechanical system, finite tightness shaft and non-linear mechanical link included. Explored system shaft has finite tightness, non-linear element - backlash between the parts of mechanical link. The researches of two - mass electromechanical system were made using Simulink program pack. In this paper I have made the structural system scheme, transmission functions and simulated process of two - mass dynamical system. Gained motor and outlet shaft angular rotation speed and motor's electromagnetic moment transitive process curves, by all tightness and backlash worth' s. Researched results give new information about the two - mass electromechanical system' s dynamical process.

Darbo metu apžvelgiami metodai pereinamiesiems procesams vamzdyne realizuoti. Aprašyta vamzdyno tėkmės pereinamųjų procesų dinamika matematinės lygtys ir sudarytas baigtinių elementų modelis skaitiniam vamzdynų pereinamųjų procesų modeliavimui. Panaudojant atgalinį slėgio bangos modeliavimą esant idealizuotam slėgio bangos sklidimo modeliui, sudaromas slėgio impulso vietos nustatymo algoritmas ir įvertinamos atsirandančios paklaidos. Realizuota programine įranga patikrinamas sudarytų modelių ir algoritmo teisingumas, bei pateikiami pasiūlymai, atsiradusioms paklaidoms mažinti. / During this research, the methods to realize the transient processes in piping systems are overviewed, also finite element method and idealized wave propagation of pressure mathematical models are set up. Using the backward pressure wave modelling at idealized pressure wave propagation model, piping system rupture location algorithm and the assessment of estimated errors are set up. With released software, the developed models and correctness of the algorithm are verified, and suggestions to reduce the resulting errors are presented.