In Figure $2,$ a $2\mathrm{.}50$ kg uniform disk of diameter $D=42\mathrm{.}0cm$ is supported by a uniform rod of length $L=76\mathrm{.}0cm$ and mass $m=1\mathrm{.}0kg$ that is pivoted at its end. $($a$)$ With the massless torsion spring unconnected, what is the period of oscillation? $($b$)$ With the torsion spring connected, the rod is vertical at equilibrium. What is the torsion constant of the spring if the period of oscillation has been decreased by $0\mathrm{.}500$ s $?(20$ points$)$