Tapping-mode scanning force microscopy in liquids is usually accomplished by acoustic excitation of the cantilever because of the strong viscous damping. Contact of the tip with the sample surface results in a damping of the cantilever amplitude with an anharmonic response. This interaction is modeled as a viscous-damped, one-dimensional harmonic oscillator periodically perturbed by an exponential surface potential. Experimental results verify the validity of the model.