We have investigated terahertz (THz) frequency magnetoplasmon resonances in a two-dimensional electron system through the direct injection of picosecond duration current pulses. The evolution of the time-domain signals was measured as a function of magnetic field, and the results were found to be in agreement with calculations using a mode-matching approach for four modes observed in the frequency range above 0.1 THz. This introduces a generic technique suitable for sampling ultrafast carrier dynamics in low-dimensional semiconductor nanostructures at THz frequencies.