Answer
$k=31N/m$
Work Step by Step
Recall that the formula relating the period with the mass and spring constant of a spring is $$T=2\pi \sqrt{\frac{m}{k}}$$ Solve for the spring constant $k$ to get $$\frac{T}{2\pi}=\sqrt{\frac{m}{k}}$$ $$\frac{T^2}{4\pi^2}=\frac{m}{k}$$ $$k=\frac{4\pi^2m}{T^2}$$ Substitute known values of $T=0.77s$ and $m=0.46kg$ to get a spring constant of $$k=\frac{4\pi^2(0.46kg)}{(0.77s)^2}=31N/m$$
