The figure shows the cross section of a uniform200-lb ventilator door hinged about its u...

The figure shows the cross section of a uniform200-lb ventilator door hinged about its upper horizontal edge at O. The door is controlled by the spring-loaded cable which passes over the small pulley at A. The spring has a stiffness of 15 lb per foot of stretch and is undeformed when θ = 0. If the door is released from rest in the horizontal position, determine the maximum angular velocity ω reached by the door and the corresponding angle θ.