Abstract: The applications of direct treatment anddiscretizations of non-linear dynamics are investigated in thispaper. These two approaches are applied to attack the primaryresonance of the nth mode of suspended cables. These lead toobtain the second order approximate solutions and the associatedfrequency-response curves. The results obtained with these twoapproaches are compared. And the differences of these results arediscussed. Finally, the results are obtained that thediscretization of nonlinear dynamic of non-symmetric structure maylead to erroneous results.