The figure shows the cross section $\backslash ($ A B $\backslash )$ of a garage door which is a rectangular $\backslash (2\mathrm{.}30-\backslash$mathrm$\{$m$\}\backslash )$ by $\backslash (5\mathrm{.}9-\backslash$mathrm$\{$m$\}\backslash )$ panel of uniform thickness with a mass of $195$ kg $.$ The door is supported by the struts of negligible mass and hinged at $\backslash ($ O $\backslash ).$ Two spring$-$and$-$cable assemblies, one on each side of the door, control the movement. When the door is in the horizontal open position, each spring is unextended. If the door is given a slight imbalance from the open position and allowed to fall, determine the value of the spring constant $\backslash ($ k $\backslash )$ for each spring which will limit the angular velocity of the door to $\backslash (1\mathrm{.}7\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$ when edge $\backslash ($ B $\backslash )$ strikes the floor.

Answer: $\backslash ($ k$=\backslash )\backslash (\backslash$mathrm$\{$N$\}/\backslash$mathrm$\{$m$\}\backslash )$