Cold plasma theory is used to calculate the response of an ultracold neutral plasma to an applied rf field. The free oscillation of the system has a continuous spectrum and an associated damped quasimode. This quasimode dominates the driven response and is resonant in the tail of the density distribution. Recent experiments used the plasma response to an applied rf field to determine the plasma density in an expanding ultracold plasma. The comparison between experiment and theory indicates that this method accurately determines the expansion velocity and underestimates the initial plasma density by a factor of 3 in weakly collisional plasmas.