The uniform garage door AB shown in section has a mass m and is equipped with two of the spring- loaded mechanisms shown, one on each side of the door. The arm OB has negligible mass, and the upper corner A of the door is free to move horizontally on a roller.
The unstretched length of the spring is r - a, so that in the top position with () = 7T the spring force is zero.
To ensure smooth action of the door as it reaches the vertical closed position () = 0, it is desirable that the door be insensitive to movement in this position.
Determine the spring stiffness k required for this design.
