Using non-dimensional variables, the performances of friction dampers of a mistuned bladed disk assembly are examined for different types of excitation: white noise excitation, independent narrow band random excitation and sinusoidal excitation with unknown amplitudes. Based on the harmonic balance method, an analytical technique is developed to compute the statistics of response for sinusoidal excitation with unknown amplitudes. The performances of blade-to-blade and blade-to-ground dampers are compared under different types of excitation. It is found that non-dimensional optimal normal loads of friction dampers are almost independent of the nature of excitation. Therefore, optimal normal loads of friction dampers can be chosen without any knowledge of the nature of excitation.