The dynamics of a driven oscillator, consisting of a cylindrical container suspended by springs and filled with a large number of freely moving balls, is investigated around the principal resonance frequency. The theoretical findings are applied to a cantilever resonance vibratory mill and allow for the experimental determination of the dynamical properties of the mill, estimation of the power input and its absorbed and dissipated fractions. The results are tested for the mechanical activation of quartz. (C) 2014 Elsevier Ltd. All rights reserved.