We study, numerically and analytically the dynamics of passive energy transfer from a damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused either by fundamental or subharmonic resonance capture, and in some cases is initiated by nonlinear beat phenomena. It is shown that, due to the essential nonlinearity, the end attachment is capable of passively absorbing broadband energy both at high and low frequencies, acting, in essence, as a passive broadband boundary controller. Complicated transitions in the damped dynamics can be interpreted based on the topological structure and bifurcations of the periodic solutions of the underlying undamped system. Moreover, complex resonance capture cascades are numerically encountered when we increase the number of degrees of freedom of the system. The ungrounded, essentially nonlinear end attachment discussed in this work can find application in numerous practical settings, including vibration and shock isolation of structures, seismic isolation, flutter suppression and packaging.

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