Interactions between buildings and earthquakes have been studied for a long time, and there is much literature about them. This research deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to control the vibrations; dry friction has also been considered. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method. From this theoretical standpoint, we derive many important analytical or numerical results, providing us the tools suitable for the design of absorbers in practical cases.