ABSTRACT Many types of velocity oscillations are observed in the umbrae and penumbrae of sunspots. We describe a project aimed at determining the source of one type of oscillation, the five-minute period photospheric umbra oscillations. The project uses imaging spectroscopy of spot umbrae, measuring the Doppler shift of pure umbral absorption lines to study the temporal and spatial properties of these oscillations. The Mees CCD (MCCD) instrument is an imaging spectroscopy device which uses the 25-cm coronagraph telescope and the 3.0-m coude spectrograph at Mees Solar Observatory (MSO) on Haleakala, Maui. The instrument works with resolving power up to R ~ 200,000 with significant throughput from lambda-3934 A (Ca II K) to lambda ~ 10,000 A. A fast guiding active mirror stabilizes the image during observations. A rapidly writing magnetic tape storage system allows observations to be recorded at 256 kbytes s-1. We observed the oscillations in the umbrae of two sunspots using the MCCD imaging spectrograph. We observed the Doppler shifts of 18 molecular lines in the umbrae for roughly 50 hours in each spot during the interval of 11 to 16 May 1991. We find no simple correlation between the velocity measured with molecular lines and the velocity measured using two iron lines. We remove solar rotation, image drift, and interpolate all the data onto an even time grid. We perform four spatial analyses of the umbral velocity and find (1) there is more power traveling toward the center of the umbrae than leaving the center of the umbrae (this provides a direct measure of the absorption of p-modes by the sunspot umbrae) (2) the umbral oscillations have spatial and temporal characteristics indistinguishable from the quiet-sun oscillations, (3) a Fourier-Bessel analysis shows no obvious resonant frequencies which might represent natural oscillation modes of the sunspot umbrae, and (4) the centers of the umbrae have less RMS velocity than the edge of the umbrae. >From these analyses we conclude that the photospheric umbral oscillations are driven by an external source and that source is the global p-mode oscillations.