We apply linear-response analysis to the Gross-Pitaevskii equation to
obtain the excitation frequencies of a Bose-Einstein condensate in a v
ortex state, and apply it to a system of rubidium atoms confined in a
time-averaged orbiting potential trap. The excitation frequencies of a
vortex differ significantly from those of the ground state, and may t
herefore be used to obtain a spectroscopic signature of the presence o
f a vortex state.