Question 2: Suppose in Question #1 that the hoop is spinning faster so flat a. a.) Show that bead can have new equilibrium pointsin addition to those identified in Question #1. Can any of these new equilibrium points satisfy> /2 (rad)? Why or why not? b.) Show that the A matrix for the linearized dynamics about each of the equilibium points in a.) has the same structure identified above, and give an explicit equation for k in terms ofa, 2, and 0*. c.) Suppose the bead is started sliding with a small initial speed and an initial angle near, but not at, zero (ie. the bead starts near the bottom of the hoop). Will the bead tend to slide down to the bottom of the hoop (ie. converge to the equilibrium)? Compare with your answer to #c.