The paper presents the new way of identification of complex non-linear dynamic systems. The method has been explained with the use of a dynamic structure (degenerated one) with 1.5 degrees of freedom and some non-linear restitution force. The applied method allows for the assessment of the dynamic behavior of material in a wide range of dynamic loads. The equation of energy balance when oscillations are set harmonic is applicable to the solution. It is possible when the loading force is adjustable. The method has been computer verified using a system with cubic spring characteristic.