Terahertz (THz) time-domain spectroscopy provides insight into electron dynamics in semiconductor heterostructures. High-field THz spectroscopy probes the excitonic nonlinear response of GaAs quantum well (QW) systems and enables the measurement of its coherent dynamics in the time-domain. Consequently, THz spectroscopy allows one to explore the fundamental properties of many-body interactions as well as the potentials of semiconductor nanodevice technology. This work analyzes the light-matter interaction in a semiconductor microcavity with a computational approach. When an exciton in a QW microcavity strongly couples with a cavity photon, a new quasiparticle known as exciton-polariton forms. This thesis shows that classical coupled harmonic oscillators with optical and THz excitations can be used as a model to simulate the dynamics of exciton-polariton and its quantum coherent phenomena. The time evolution of the exciton-photon coupled system is demonstrated by employing the time-dependent damping of the exciton mode and varying the delay between optical and THz pulses. The normal mode splitting is observed in the frequency spectra as a result of strong light-matter hybridization. Finally, computed exciton-polariton oscillation of this work is compared to the computed result from a reference which was obtained using a semiconductor Bloch equations.