Reconsider the door of Prob. 6/144. If the door is in the closed vertical position when a constant input force P = 225 N is applied through the end of the cable, determine the maximum angle θ_max reached by the door before it comes to a stop. Plot the angular velocity of the door over this period and determine the maximum angular velocity of the door along with the corresponding angle θ at which it occurs. The uniform door has a mass m = 40 kg, dimension b = 1.25 m, and the spring constant is k = 2280 N/m.