Answer
$K=7.9\frac{N}{m}$
Work Step by Step
We know that,
$\omega=\sqrt\frac{K}{m}$
After squaring both sides and rearranging, we obtain:
$K=\omega^2m$ .................eq(1)
We also know that,
$\omega=\frac{2\pi}{T}$
As $T=0.5s$,
$\omega=\frac{2\pi}{0.5}=4\pi\frac{rad}{s}$
We plug in the known values to obtain:
$K=(4\pi)^2(0.05)$
$K=7.9\frac{N}{m}$
