A bead of mass m slides without friction on a smooth rod along the x axis. The rod is equidistant between two spheres of mass M. The spheres are located at x = 0, y = ±a as shown, and attract the bead gravitationally.
a. Find the potential energy of the bead.
b. The bead is released at x = 3a with velocity v0 toward the origin. Find the speed as it passes the origin.
c. Find the frequency of small oscillations of the bead about the origin.
