A 0.2-kg spool slides down along a smooth rod. If the rod has a constant angular rate of...

A 0.2-kg spool slides down along a smooth rod. If the rod has a constant angular rate of rotation  in the vertical plane, show that the equations of motion for the spool are  and  where Ns 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 = C1 e-2t + C2e2t - (9.81/8) sin 2t. If r,   and θ are zero when t = 0, evaluate the constants C1 and C2 determine r at the instant θ = π/4 rad.