Analysis of dynamic sensing of force between a probe and a vibrating sample for purposes of atomic force microscope

Using a perturbation method, we study the influence of the vibration of the sample on the resonance curve of a probe. The obtained resonance curve indicates that both the resonance frequency shift and the vibration amplitude of the probe are proportional to the gradient of the interaction force between the probe and the sample, even if the probe is not forced to vibrate by an external force. For several surface forces such as the Casimir force, which are described by power functions, we show that the frequency shifts obtained by the perturbation method agree well with those obtained by numerical simulations.