The cylinder of mass m is held in the equilibrium confi guration by means of three light

Chapter 7, Problem 7/73

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The cylinder of mass m is held in the equilibrium configuration \(\theta\) by means of three light links and a nonlinear spring near E. The spring is uncompressed when link OA is vertical, and the potential energy in the spring is given by \(V_e=k \delta^3\), where \(\delta\) represents the amount of spring deformation from the uncompressed position and the constant k is related to the stiffness of the spring. As \(\theta\) increases, the rod, which is connected at A, slides through the pivoted collar at E and compresses the spring between the collar and the end of the rod. Determine the values of \(\theta\) for system equilibrium over the range \(0 \leq \theta \leq 90^{\circ}\) and state whether the system is stable or unstable in those positions for \(k=35 \mathrm{~N} / \mathrm{m}^2\), b = 600 mm, and m = 2 kg. Assume no mechanical interference for the indicated range of motion.