The collar of mass m slides on the rough horizontal shaft under the action of the force F of constant magnitude F ≤ mg but variable direction. If θ = kt where k is a constant, and if the collar has a speed v₁ to the right when θ = 0, determine the velocity v₂ of the collar when θ reaches 90°. Also determine the value of F which renders v₂ = v₁.

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F m