The dynamics of a short-cavity, electrooptically tunable microchip laser is studied using the Maxwell-Bloch equations for a unidirectional ring cavity. Within this model, the electrooptic tuning medium is treated rigorously by a wave propagation equation and the electrooptic tuning is equivalent to introducing a time varying perturbation to the boundary condition. With the help of an approximate analytic solution as well as numerical simulations, we find that the laser relaxation does not pose limitations to the intracavity frequency modulation bandwidth. Instead, the bandwidth is a sensitive function of the cavity length and also of the fraction of the cavity length taken up by the electrooptic section. In addition, under large-signal sinusoidal modulation, the numerical solutions reveal complicated dynamical behaviors when the modulation frequencies are near the cavity free spectral range.