Answer
$$ k=100 \mathrm{lb} / \mathrm{ft}
$$
Work Step by Step
$$
\begin{aligned}
& (2)^2=(6)^2+(C D)^2-2(6)(C D) \cos 15^{\circ} \\
& C D^2-11.591 C D+32=0
\end{aligned}
$$
Selecting the smaller root:
$$
\begin{aligned}
& C D=4.5352 \mathrm{ft} \\
& T_1+V_1=T_2+V_2 \\
& 0+0=0+2\left[\frac{1}{2}(k)(8-4.5352)^2\right]-200(6) \\
& k=100 \mathrm{lb} / \mathrm{ft}
\end{aligned}
$$
