The forked rod is used to move the smooth particle of weight W around the horizontal path in the shape of a limacon r = a + bcosθ. If θ = ct², determine the force which the rod exerts on the particle at the instant t = t₁. The fork and path contact the particle on only one side.

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Given: W = 2 lb a = 2 ft b = 1 ft C c = 0.5 rad 2 S