Answer
$90.81lb.ft/rad$
Work Step by Step
We know that
$\omega_n=\sqrt{\frac{K_{eq}}{m_{eq}}}$
$\implies \omega_n=\sqrt{\frac{K}{0.207}}$..eq(1)
We also know that
$T=\frac{2\pi}{\omega_n}$
$\implies \omega_n=\frac{2\pi}{T}=\frac{20}{3}\pi$..eq(2)
Comparing eq(1) and eq(2), we obtain:
$\frac{20}{3}\pi=\sqrt{\frac{K}{0.207}}$
This simplifies to:
$K=90.81lb.ft/rad$
