Ultracold plasmas (UCP) provide a well-controlled system for studying multiple aspects in plasma physics that include collisions and strong coupling effects. By applying a short electric field pulse to a UCP, a plasma electron center-of-mass (CM) oscillation can be initiated. In accessible parameter ranges, the damping rate of this oscillation is determined by the electron-ion collision rate. We performed measurements of the oscillation damping rate with such parameters and compared the measured rates to both a molecular dynamic (MD) simulation that includes strong coupling effects and to Monte-Carlo collisional operator simulation designed to predict the damping rate including only weak coupling considerations. We found agreement between experimentally measured damping rate and the MD result. This agreement did require including the influence of a previously unreported UCP heating mechanism whereby the presence of a DC electric field during ionization increased the electron temperature, but estimations and simulations indicate that such a heating mechanism should be present for our parameters. The measured damping rate at our coldest electron temperature conditions was much faster than the weak coupling prediction obtained from the Monte-Carlo operator simulation, which indicates the presence of significant strong coupling influence. The density averaged electron strong coupling parameter $Gamma$ measured at our coldest electron temperature conditions was 0.35.
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