We study the dynamics of an atomic force microscope (AFM) model, under the Lennard‐Jones force with nonlinear damping and harmonic forcing. We establish the bifurcation diagrams for equilibria in a conservative system. Particularly, we present conditions that guarantee the local existence of saddle‐node bifurcations. By using the Melnikov method, the region in the space parameters where the homoclinic orbits persist is determined in a nonconservative system.