1. The potential energy of a mechanical system is given by V = 6x4 - 3x2 + 5, where x is the position coordinate which defines the configuration of the single-degree-of-freedom system. Determine the equilibrium values of x and the stability condition of each.
2. For the mechanism shown the spring is uncom- pressed when () = 0. Determine the angle () for the equilibrium position and specify the minimum spring stiffness k which will limit () to 30°. The rod DE passes freely through the pivoted collar C, and the cylinder of mass m slides freely on the fixed vertical shaft.