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The dynamic behavior of AFM is studied taking into account the nonlinearinteraction forces between probe and sample. The exerted forces on the free endof micro-beam are simulated with the third degree polynomial. The effect ofsome parameters on the dynamics of AFM is studied. The results show that thefrequency response of AFM is not sensitive to the tip mass in the case of boththe sample and cantilever vibration. The effect of sample vibration is studiedin the case of in-phase and anti-phase vibration. The results show thatalthough the vibration amplitude of sample is very small compared to theamplitude of cantilever, it has great effect on the resonant frequency of thecantilever.

An analytical solution for nonlinear dynamics of one kind of scanning probe microscopes