The time dependence of the weak field microwave absorption spectrum of the J = 1 → 2 transition of OCS under amplitude modulated pumping of the J = 0 → 1 transition has been observed with submicrosecond resolution by using a 100 MHz bandwidth video spectrometer and a multichannel signal averager. In order to relate the observed time dependent power absorption to the dynamic process of rotational energy transfer a theory relating the power absorption and the energy level populations has been developed. It is found that the time variation of the power absorption is not simply proportional to time variation of the population difference between the two levels connected by the weak field. Equations are derived which describe the time evolution of these quantities immediately following inception and termination of the pump signal. It is found that, for practical reasons, the period immediately following termination of the pump signal is the best time to study collisional energy transfer. Observation of the pressure dependence of the absorption relaxation during this period led to a value of Pτ = 28.1 μ · μsec for the product of the pressure and the mean time between rotationally inelastic collisions.