When the two pendulum are joint rigidly and set to oscillate, each exert torques on the other, these torques are equal and opposite . We write the l;aw of motion for the two pendulum I1¨θ=−ω21I1θ+G
I2¨θ=−ω21I2θ−G
where ±G is the torque of mutual interaction. We have writtten the restoring forces on each pendulum in the absence of the other as −ω21I1θ−G and −ω22I2θ−G respectively. Then
¨θ=−−ω21I1θ+ω22I2θI1+I1θ=−ω2θ
Hence ω=√−ω21I1θ+ω22I2θI1+I1θ