The application of Tuned Mass Dampers in mechanical engineering is of longstanding and habitual use. In these kinds of applications, the loading forces are based on constant frequencies and they are in most case well known. The application of a TMD in structural engineering is more recent, beginning a few years ago under the concept of seismic protection. The design of a TMD for a building presents the practical difficulty of tuning the device to the fundamental period of the structure. Through the application of additional damping, it is possible to widen the range of tuning frequencies and therefore increase the effectiveness of the TMD. Additionally, the seismic loads to which the structure will be submitted are uncertain in their frequency distribution which could generate a counterproductive effect, because the response of the building to the seismic forces could be even worse with the use of TMD. The addition of more damping has the result of a reduction of the positive effect of the TMD at the fundamental frequency, but produces a better response for the entire range of frequencies of the seismic excitation. The following work shows both the theoretical and practical application of this concept to a building built in 2006 in Santiago de Chile, which passed unscathed the 2010 Maule Earthquake, which reached a magnitude 8,8 Mw with an intensity VIII in the locations of the building.