Answer
140 N/m
Work Step by Step
Let's apply the equation $\omega=\sqrt {\frac{k}{m}}$ to find the value of k.
$\omega=\sqrt {\frac{k}{m}}=>k=\omega^{2}m-(1)$
We know that,
$T=\frac{2\pi}{\omega}=>\omega=\frac{2\pi}{T}-(2)$
(2)=>(1),
$k=(\frac{2\pi}{T})^{2}m$ ; Let's plug known values into this equation.
$k=\frac{4\pi^{2}\times82\space kg}{4.8^{2}\space s^{2}}\approx140\space N/m$
