Dynamic force microscopy is a powerful tool to image non-conductive materials with atomic resolution using the nonlinear interaction force. A perturbation method is extended to analyze the nonlinear oscillation dynamics of the frequency modulation dynamic force microscopy. A general resonant frequency shift formula is derived for both conservative and dissipative interaction forces, and validation conditions are provided. Furthermore, the approximate motions of higher resonances are derived, which provide in depth analysis of force-motion relation, and can be applied for force sensing when amplitudes of higher resonances are measurable.