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We present an experimental investigation of the variation of the amplitude of vibrating microcantilever, as a function of distance (h) between the microcantilever and the sample in a Dynamic Force Microscopy (DFM) and explain the observations with a theoretical model. In DFM, as the cantilever tip approaches the sample, neither the force nor the response of the cantilever is in the linear regime. We present an exact numerical solution to the equation of motion of the oscillations of the microcantilever and present a quantitative explanation to the observed force versus distance curves, in terms of the resonance curves. We show that the change in the resonance frequency of the cantilever due to the atomic forces is highly nonlinear.