We present an algorithm which allows us to identify all possible stable states of the cantilever oscillation of an AFM operated in the intermittent contact mode within the harmonic approximation. The oscillatory states are qualified as quasi-free, net-attractive and net-repulsive solutions. Using a generic model for the tip-sample interaction the influence of a number of important experimental parameters on the state of oscillation is systematically studied. The analysis gives conditions under which an AFM can be operated in a chosen state. As an exemplary experimental application we compare selected measurements on a semicrystalline polymer acquired in the net-repulsive and the net-attractive mode with simulations based on the approach introduced here. The experiments indicate that a small indentation below one nanometer in the net-attractive mode is enough to produce phase contrast.