AbstractIt is shown that two of the damping ratios of certain systems composed of a building and a small attachment in resonance are given by the average of the damping ratios of the two independent components. Based on this fact and the fact that the seismic response of a building can always be reduced by increasing its damping, it is demonstrated that the attachment of a small heavily‐damped system in resonance can increase the damping of a building and reduce thus its response to earthquake excitations. Numerical solutions are presented to confirm the demonstration, and recommendations are given to calculate the parameters of such system