The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to
a lightweight mass by means of a spring with both cubic nonlinear and negative linear components
is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator,
excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped
systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well
oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics
evolves solely in-well. The description of the former dissipative phenomenon is provided in a
two-dimensional projection of the phase space, where transitions between in-well and cross-well
oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second
mechanism is described in terms of secondary limiting phase trajectories of the nonlinear
attachment under certain resonance conditions. The analytical treatment of the two aformentioned
low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent
analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully
validate our analytical predictions
