The motion of the uniform 80-lb garage door is guided at its ends by the track. Determine...

The motion of the uniform 80-lb garage door is guided at its ends by the track. Determine the required initial stretch in the spring when the door is open, θ = 0°, so that when it falls freely it comes to rest when it just reaches the fully closed position, θ = 90°. Assume the door can be treated as a thin plate, and there is a spring and pulley system on each of the two sides of the door.