We determine conservative and dissipative tip-sample interaction forces from the amplitude and phase response of acoustically driven atomic force microscope (AFM) cantilevers using a non-polar model fluid (octamethylcyclotetrasiloxane, which displays strong molecular layering) and atomically flat surfaces of highly ordered pyrolytic graphite. Taking into account the base motion and the frequency-dependent added mass and hydrodynamic damping on the AFM cantilever, we develop a reliable force inversion procedure that allows for extracting tip-sample interaction forces for a wide range of drive frequencies. We systematically eliminate the effect of finite drive amplitudes. Dissipative tip-sample forces are consistent with the bulk viscosity down to a thickness of 2-3 nm. Dissipation measurements far below resonance, which we argue to be the most reliable, indicate the presence of peaks in the damping, corresponding to an enhanced 'effective' viscosity, upon expelling the last and second-last molecular layer.
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