13.92, A large bell is hung from a wooden beam so it can swing back and forth wi

Question

13.92, A large bell is hung from a wooden beam so it can swing back and forth with a negligible friction.The canter of mass of the bell is .60 m below the pivot, the bell has mass 34.0 kg, and the moment of inertia of the bell about an exit at the pivot is 18.0 kg.m^2.  The clapper is a small, 1.8-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? Please walk me steps!

Explanation / Answer

for bell     2 = mgd / I = 34 * 9.80 * 0.60 / 18.0  =    11.10667 . for the rod,    2 = g / L       . and this should be the same as for the bell,so...         11.10667 = 9.80 / L .         L =    0.882 meters

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