This paper presents new results on the behaviour of an n-link pendulum which is controlled by means of an oscillatory input forcing one end link. Drawing on recent research on the oscillatory control of second order non-linear systems, we adopt the averaged potential as the primary tool in our equilibrium and stability analysis. While such control of single-degree-of-freedom systems has been studied in fair detail by Weibel and Baillieul, researchers are only beginning to explore the issues which arise in the control of multi-degree-of-freedom systems. Of specific interest is the behaviour when the system possesses bifurcations and more than one stable equilibrium. In this paper, we present a study of the bifurcations and stability of a periodically forced cart and n-pendulum on an inclined plane. Periodic open-loop forcing of the single degree-of-freedom pendulum has previously been shown to be a robust and effective means of stabilizing the inverted equilibrium, and this robustness carries over to the multi-degree-of-freedom case provided attention is paid to matching the forcing amplitude to the characteristic length scales of the system. In addition, we present numerical results on the basins of attraction of the vertically forced double pendulum. We present an exact model for the n-degree-of-freedom system, non-dimensionalize the model, and compute the averaged potential. Equilibria and their stability characteristics are found through a bifurcation analysis of the averaged potential. For a double pendulum system, we are able to provide a detailed comparison of analytical, numerical and experimental results-all of which are found to be in close agreement.