  We study a system consisting of a particle adsorbed on a carbon nanotube
resonator. The particle is allowed to diffuse along the resonator, in order to
enable study of e.g. room temperature mass sensing devices. The system is
initialized in a state where only the fundamental vibration mode is excited,
and the ring-down of the system is studied by numerically and analytically
solving the stochastic equations of motion. We find two mechanisms of
dissipation, induced by the diffusing adsorbate. First, short-time correlations
between particle and resonator motions means that the net effect of the former
on the latter does not average out, but instead causes dissipation of
vibrational energy. For vibrational amplitudes that are much larger than the
thermal energy this dissipation is linear; for small amplitudes the decay takes
the same form as that of a nonlinearly damped oscillator. Second, the particle
diffusion mediates a coupling between vibration modes, enabling energy transfer
from the fundamental mode to excited modes, which rapidly reach thermal
equilibrium.
