The work begins by presenting the main concepts related to the dynamics of mechanical systems, with one and multiple degrees of freedom, aiming at the analytical modeling and numerical simulation of such systems, in order to understand how they behave under the action of external forces. The work focuses on a method called modal decomposition, which consists in determining the modal parameters (natural frequencies and vibration modes) of a system and in decomposition of the dynamics using these modal parameters. The objective is to determine how these parameters influence it. A tool that is used to perform this procedure is the frequency response function (FRF) matrix of the system, whose elements are denoted as a function of modal parameters. From the knowledge of the elements of the FRF matrix, one can determine how a mechanical system behaves when subjected to external forces. The topics related to the theory of modal analysis are applied to a mechanical system with five degrees of freedom, whose study is divided into two cases: without damping and with linear viscous damping. Both cases were simulated using MatLab software, in time and frequency domains. From the results obtained, it is possible to verify the main concepts related to the theory of modal analysis and, to understand how a mechanical systemnbehaves under external loads.