The ring at $B$ is supported in equilibrium by spring $AB,$ a cable running through the frictionless pulley at $C,$ and cable $BD.$ The pulley radius is $0\mathrm{.}0200$ m $,$ and the unstretched length of spring $AB$ is $0\mathrm{.}28$ m $.$ If $F_1=400N$ and $F_2=120N$ at $=36$ degrees, determine the spring constant $k$ and the force exerted on the $.$ ring by cable $BD$ expressed in Cartesian components.

Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.

$\backslash$table$[[$Variable$,$Value$],[a,0\mathrm{.}400$ m$],[b,0\mathrm{.}120$ m$],[c,0\mathrm{.}200$ m$],[d,0\mathrm{.}0800$ m$]]$

Note the figure may not be to scale.

$k=,\frac{N}{m}$

vec$(F{)}_{BD}=,$hat$(i)+,$ hat$($j$)$ N