A large bell is hung from a wooden beam so it can swing back and forth with negligible friction. The center of mass of the bell is 0.70{\rm m} below the pivot, the bell has mass 34.0{\rm kg} , and the moment of inertia of the bell about an axis at the pivot is 20.0{\rm kg \cdot m^{2}} . The clapper is a small, 1.8 {\rm kg} mass attached to one end of a slender rod that has length L and negligible mass. The other end of the rod is attached to the inside of the bell so it can swing freely about the same axis as the bell.
What should be the length L of the clapper rod for the bell to ring silently-that is, for the period of oscillation for the bell to equal that for the clapper?