<p>Autoparametric resonance in a combined contact (tip apex)–driving-spring (cantilever) system, that is responsible for the appearance of multiple peaks in friction as a function of scanning velocity, is investigated in a wide range of the possible system damping. The role of cantilever damping, being practically inessential in conventional stick–slip regime at lower velocities, is shown to be crucial for the appearance of friction force peaks at the resonant and quasi-resonant velocities. With changing damping, the evolution of different peaks turns out to be nontrivial, that is related with an unusual manifestation of double slips of the tip and memory effects. Relative value of the main force peaks as functions of damping factor are non-monotonous with maximum, which can reach several tens percent, depending on the system parameters and temperature. Such a strong resonance enhancement of energy dissipation is likely to occur in practical systems, where damping of driving spring can be significant, in contrast to nearly ideal cantilevers used in AFM experiments.</p> Graphical Abstract <p></p>