oscillators. The instantaneous frequency was calculated using an Hilbert transform [@Worden-Tomlinson].

For $\mathcal{H}_0 = 15$ (figures \[fig:TransH15-x\] and \[fig:TransH15-v\]), the input of energy is smaller than the bifurcation characteristic level. Hence, as predicted by the nonlinear modes (see figure \[fig:ModesNL1\]) and in accordance with the initial conditions, only the solid line branch of the modes is realizable. This means that the vibratory energy remains in the main oscillator: no energy pumping occurs.

For $\mathcal{H}_0 = 60$ (figures \[fig:TransH60-x\] and \[fig:TransH60-v\]), the initial energy is greater than the critical bifurcation level. As a consequence, the dashed line branch in figures \[fig:ModesNL1\] is feasible. The energy is rapidly transferred from the main mass to the absorber. To confirm the predictions of the nonlinear modes, we can watch the history of the instantaneous frequency: in the early moments (after a short transient period), the instantaneous frequencies from the linear and nonlinear oscillator join, then (as the global energy decreases) both of them increase. This is in accordance with the evolution of the nonlinear natural frequencies of the modes.

Steady-State Forced Response {#sect:ForcedResp}
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This final part is dedicated to forced resonance phenomena. We were, in particular, interested in periodically forced regimes. In contrast 