The equation of motion of a grazing impact oscillator is generalized to include compliant boundaries and impact energy dissipation, yielding the phase diagram, indentation and force. Good agreement with experimental results using tapping-mode atomic force microscopy is demonstrated. The relationship between phase and set-point amplitude is discussed in terms of the dissipation, showing that for a parameter space for which the system is highly nonlinear a chaotic response is possible. ©1998 American Institute of Physics.