Q$1(10$ points$)$

The left end of a spring of spring constant $k,$ is attached to a wall, while its right end is attached to a solid disk of mass $M$ and radius $R$ at a radial distance $r=\frac{R}{2}$ directly above the disk's centre of mass. The disk is free to rotate without friction about a fixed axis of rotation passing through its centre of mass and perpendicular to the plane of the disk. The figure shows the disk and spring in its equilibrium position. If the disk is initially displaced from equilibrium, find the period of small angle oscillations $($SHM$).$

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$59$:$29$