A simple model of orbital motion under a central force can be constructed by considering the motion of a disk D sliding with no friction over a horizontal surface while connected to a fixed point O by a linear elastic cord of constant k and unstretched length { L }_{ 0 }. Let the mass of D be m = 0.45 kg and { L }_{ 0 } = 1 m. Suppose that when D is at its maximum distance from O, this distance is { r }_{ 0 } = 1.75m and the corresponding speed of D is { \upsilon }_{ 0 } = 4m/s. Determine the elastic cord constant k such that the minimum distance between D and O is equal to the unstretched length { L }_{ 0 }.