Energyexchangesbetweenparticlesofatwodegreesoffreedom- dof meta-cell are studied. The nondimensionalized equations of the sys- tem are presented and then complexified. Only the first harmonics of the system are kept before applying a time multiple scales method. Detec- tion of system dynamics at different time scales leads to the clarification of the slow invariant manifold and characteristic points of the system. Finally, frequency response curves of the system are presented and quasi- analytical responses are confronted with numerical ones obtained by time direct integration.