The transient response of a contained stratified rapidly rotating fluid to an impulsive surface stress has been studied theoretically and experimentally. The analysis predicts, and the experiments confirm. that for low values of the Burger number S the initial fluid adjustment within the E-1/2OMEGA-1 timescale is characterized by a barotropic response in which the magnitude of the interior velocity is independent of depth. (Here E and OMEGA are the Ekman number and rotation rate respectively.) The period of the barotropic response decreases as S increases. For large S, the barotropic flow adjusts subsequently to a baroclinic flow within the E-1/2OMEGA-1 scale, and during this later stage the excess and deficit in velocity in the lower and upper parts respectively of the fluid are removed. The baroclinic flow forced by the surface stress in these cases is thereby established in a timescale which is typically less than the spin-up time for a homogeneous fluid. The agreement between theory and experiment is shown to be qualitatively good, and the quantitative discrepancies observed between the predicted and measured interior velocities are discussed.