There is a demand for good theoretical understanding of the response o
f an atomic force microscope cantilever to the extremely nonlinear imp
acts received while tapping a sample. A model and numerical simulation
s are presented in this paper which provide a very pleasing comparison
with experimental results. The dependence of the cantilever amplitude
and phase upon the sample stiffness, adhesion and damping are investi
gated using these simulations, and it is found that 'topographic' tapp
ing images are not independent of sample properties, nor will it be tr
ivial to measure materials' properties from the tapping data. The simu
lation can be applied to other probe microscope configurations as well
.