$-$ Problem Statement

The figure shows the cross section of a garage door which is a uniform rectangular panel $8$ ft by $8$ ft and weighing $200$ lb $.$ The door carries two spring assemblies, one on each side of the door, like the one shown. Each spring has a stiffness of $\backslash (50\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash )$ and is unstretched when the door is in the open position shown. If the door is released from rest in this position, calculate the velocity of the edge at $\backslash ($ A $\backslash )$ as it strikes the garage floor.