Parameters optimization for energy pumping is considered. The case of strongly nonhomogeneous nonlinear system with 2 dof is analyzed. Damping in strongly nonlinear energetic sink as well as in the linear primary structure are taken into account. In particular efficiency of energy pumping is studied by using an analytical expression. This analytical form is obtained owing to the multiple scale analysis by using the complex variables. Analytical results are confirmed by numerical ones. An experimental verification based on a reduced-scale building model is also considered.