The Finite Difference Time Domain (FDTD) method is becoming increasingly popular for room acoustics simulation. Yet, the literature on grid excitation methods is relatively sparse, and source functions are traditionally implemented in a hard or additive form using arbitrarily-shaped functions which do not necessarily obey the physical laws of sound generation. In this paper we formulate a source function based on a small pulsating sphere model. A physically plausible method to inject a source signal into the grid is derived from first principles, resulting in a source with a nearflat spectrum that does not scatter incoming waves. In the final discrete-time formulation, the source signal is the result of passing a Gaussian pulse through a digital filter simulating the dynamics of the pulsating sphere, hence facilitating a physically correct means to design source functions that generate a prescribed sound field.