The wire described in the preceding problem is now forced to rotate about its vertical axis of
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The wire described in the preceding problem is now forced to rotate about its vertical axis of symmetry with constant angular velocity \(\Omega\).
(a) Find \(\Omega_{c}\), the critical value of \(\Omega\) for which the equilibrium point at \(x=0\) is no longer a stable equilibrium point, and find the values of \(x\) for which there is then a stable equilibrium point for the bead.
(b) Find the frequency of small oscillations of the bead about each of any new equilibrium points.
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