A two-degree-of-freedom dynamical system has been analyzed to determine an optimum control sequence which will drive the dynamical system from an arbitrary initial position and velocity to one of a prescribed set of terminal position and velocity's in minimum time. The basic complexities are: (1) that the forcing function can change only at discrete intervals of time, and (2) that the prescribed terminal states allow a multiplicity of solutions to prevail. A novel but not unique force program which is dependent upon the initial state of the system has been determined. This program consists essentially of the continuous application of a force of the proper sense and maximum allowable amplitude followed by a time during which no force is applied. This is followed by a time interval in which the forcing function has a maximum amplitude but is of the opposite sign to that used in the first part of the program.