We investigate the electron dynamics in a one-dimensional mesoscopic ring under the influence of short, linearly polarized half-cycle electromagnetic pulses. It is shown that the pulses induce a nonequilibrium coherent population of electronic states such that a time-dependent charge polarization of the ring is induced. The time-dependent charge oscillations persist after the pulses have diminished and decay on a time scale determined by the relaxation time. The overall duration of the charge polarization can be controlled by applying an appropriate train of half-cycle pulses. Furthermore, we show that the emission spectrum associated with the pulse-induced charge oscillations can be modulated appropriately by tuning the parameters of the driving pulses. It is shown theoretically how the induced charge polarization can in principle be utilized to measure experimentally the relaxation time of the system in a field-free manner.