A 0.2-kg spool slides down along a smooth rod. If the rod has a constant angular rate of rotation θ̇ = 2 rad/s in the vertical plane, show that the equations of motion for the spool are r̈  - 4r - 9.81 sin θ = 0 and 0.8ṙ + N_s - 1.962 cos θ = 0, where N_s is the magnitude of the normal force of the rod on the spool. Using the methods of differential equations, it can be shown that the solution of the first of these equations is r = C₁e^-2t + C₂e^2t - (9.81/8) sin 2t. If r, ṙ, and θ are zero when evaluate the constants C₁ and C₂ to determine r at the instant θ = π/4 rad.

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8 = 2 rad/s