  Direct time-varying tip-sample force measurements by torsional harmonic
cantilevers facilitate detailed investigations of the cantilever dynamics in
tapping-mode atomic force microscopy. Here we report experimental evidence that
the mathematical relationships describing the steady state dynamics are
quantitatively satisfied by the independent measurements of tip-sample forces
over a broad range of experimental conditions. These results confirm the
existing understanding of the tapping-mode atomic force microscopy and build
confidence on the reliability of time-varying tip-sample force measurements by
the torsional harmonic cantilevers.
