Question

what is the mass of load attached to the spring of it had a period of 0.24 seconds and a spring constant of 205.6 N/m

Answer 1

The period of a mass $m$, attached to a spring with spring constant $k$ is $T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{ \frac{m}{k}}$. From the last equation, the mass is $m = \frac{k T^2}{4 \pi^2} \approx 0.35 s$.