The system shown in the figure below consists of a uniform disk of mass $M = 2.0 \, kg$ and radius $R = 0.2 \, m$ that is equipped with a fixed, frictionless, horizontal axle and a light coiled spring (clock spring) of torsion constant $k = 10 \, Nm/rad$. Recall that when the disk is rotated through an angle $\theta$, the torsion spring exerts a restoring torque $\tau = -k\theta$. A light string is wound around the disk and a mass $m = 4.0 \, kg$ is suspended from it. The mass is pulled down and released. What is the period of the resulting oscillations? (10 marks)