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The Atomic force microscope (AFM) is an enormously valuable tool in a wide variety of applications because of its function to depict in different mediums with the sub-nano-meter resolution, and also manipulating objects with nano-meter-scale features and measuring forces with better than pico-newton resolution. In this paper, the lumped parameter model is used to construct the mathematical model of the AFM cantilever. The cantilever tip, excited by the harmonic external force, is under the influence of the tip-sample interaction force. Since, we consider the AFM in the operation mode named dynamic contact mode, the Deryagin-Muller-Toporov (DMT) force is considered as the interaction force between the cantilever tip and the surface of the sample. DMT force causes non-linearity. To solve the equation of motion, the Van der Pol method is used to obtain the frequency response equation to investigate the non-linearity effect as well as the amplitude of the excitation on the response. The stability of steady state motion is investigated.

Dynamic analysis of atomic force microscope in tapping mode