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Cantilevers with interferometric high bandwidth force sensors can resolve nonlinear tip-sample interaction forces in tapping-mode atomic force microscopy. In this paper, we provide a detailed analysis of time-resolved force measurements using such cantilever. We first model the probe as a coupled spring-mass system and investigate its steady state dynamics under tapping-mode imaging conditions. Next, we analyze the optical response of the interferometric force sensor: Diffraction patterns as a function of tip displacement are obtained both analytically and by simulations. Finally, the frequency response of the force sensor is calculated, and the effects of the sensor geometry variations on the sensor mechanical response are analyzed.