  We present an analytical solution to the dynamics of a noninteracting cloud
of thermal atoms in a cigar-shaped harmonic trap with a quartic perturbation
along the axial direction. We calculate the first and second moments of
position, which are sufficient to characterize the trap. The dynamics of the
thermal cloud differ notably from those of a single particle, with an offset to
the oscillation frequency that persists even as the oscillation amplitude
approaches zero. We also present some numerical results that describe the
effects of time-of-flight on the behavior of the cloud in order to better
understand the results of a hypothetical experimental realization of this
system.
