Answer
$m=48kg$
Work Step by Step
Remember that the formula relating the period of a mass spring system and the mass/spring constant is $$T=2\pi \sqrt{\frac{m}{k}}$$ Solving the formula for mass yields $$\frac{T}{2\pi}=\sqrt{\frac{m}{k}}$$ $$\frac{T^2}{4\pi^2}=\frac{m}{k}$$ $$m=\frac{T^2k}{4\pi^2}$$ Substituting known values of $k=2600N/m$ and $T=0.85s$ yields a mass of $$m=\frac{(0.85s)^2(2600N/m)}{4\pi^2}=48kg$$
