  Bending-mode vibrations of carbon nanotube resonator devices were
mechanically detected in air at atmospheric pressure by means of a novel
scanning force microscopy method. The fundamental and higher order bending
eigenmodes were imaged at up to 3.1GHz with sub-nanometer resolution in
vibration amplitude. The resonance frequency and the eigenmode shape of
multi-wall nanotubes are consistent with the elastic beam theory for a doubly
clamped beam. For single-wall nanotubes, however, resonance frequencies are
significantly shifted, which is attributed to fabrication generating, for
example, slack. The effect of slack is studied by pulling down the tube with
the tip, which drastically reduces the resonance frequency.
