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The uniform rod with a mass per unit length of is being pulled by the cord attached at B that passes over the smooth peg

The uniform rod with a mass per unit length of is being pulled by the cord attached at B that passes over the smooth peg at C. The magnitude of the force T is constant. The rod is hinged at O and has an angular velocity of o at the instant shown, determine the equations of motion for the rod and find the reaction force at O at the instant shown

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