In this paper, we study a problem of passive suppression of helicopter Ground Resonance (GR) using a single degree freedom Nonlinear Energy Sink (NES). GR is a dynamic instability involving the coupling of the blades motion in the rotational plane (i.e. the lag motion) and the helicopter fuselage motion. A reduced linear system reproducing GR instability is used. It is obtained using successively Coleman transformation and binormal transformation. The analysis of the steadystate responses of this model is performed when a NES is attached on the helicopter fuselage. The NES includes linear damping and essential cubic restoring force. The analysis is achieved applying complexification-averaging method and slow-fast partition of the motion. The resulting slow-flow model is finally analyzed using multiple scale approach. Four steady-state responses are highlighted and explained theoretically: complete suppression, partial suppression through strongly modulated response, partial suppression through periodic response and no suppression of the GR. An algorithm based on simple criterions is developed to predict these steady-state response regimes. Numerical simulations of the complete system confirm this analysis of the slowflow dynamics. A parametric analysis of the influence of the NES damping coefficient and the rotor speed on the response regime is finally proposed.