A uniform solid disk of mass \(M\) and radius \(R\) is mounted on a horizontal, frictionless axle. The axle passes through point \(P\), which is located a horizontal distance \(d\) from the geometric center \(C\) of the disk. The disk is initially held at rest in an orientation such that \(C\) is directly to the right of \(P\), making the line connecting \(P\) and \(C\) horizontal.

A light string is wrapped around the circumference of the disk, and the string does not slip. Block 1 of mass \(m_1\) hangs from the left side of the disk, and Block 2 of mass \(m_2\) hangs from the right side. The system is initially held at rest by a locking pin at point \(P\) that prevents the disk from rotating.