$***29.$ Two thin aluminum rods are braced and welded rigidly together at $90,$ and then pivoted at the weld so that they can rotate in the plane of the two rods, as shown in the figure at right. The rods are each $80$ cm long and have negligible mass. At the end of each rod is a small iron ball of mass $500$ g $.$ The equilibrium position for this combination of rods and balls is when each rod is $45$ from the vertical. Find the period of small oscillations of this object about its equilibrium position.