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 $n$th 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.