  We develop formalism based on the projected Gross Pitaevskii equation to
simulate the finite temperature collective mode experiments of Jin et al. [PRL
78, 764 (1997)]. We examine the $m=0$ and $m=2$ quadrupolar modes on the
temperature range $0.51T_c-0.83T_c$ and calculate the frequencies of, and phase
between, the condensate and noncondensate modes, and the condensate mode
damping rate. This study is the first quantitative comparison of the projected
Gross-Pitaevskii equation to experimental results in a dynamical regime.
