  We propose to use the damping signal of an oscillating cantilever in dynamic
atomic force microscopy as a noninvasive tool to study the vibrational
structure of the substrate. We present atomically resolved maps of damping in
carbon nanotube peapods, capable of identifying the location and packing of
enclosed Dy@C82 molecules as well as local excitations of vibrational modes
inside nanotubes of different diameter. We elucidate the physical origin of
damping in a microscopic model and provide quantitative interpretation of the
observations by calculating the vibrational spectrum and damping of Dy@C82
inside nanotubes with different diameters using ab initio total energy and
molecular dynamics calculations.
