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#4 Thickness d 7 20 20- The planar system shown consists of a circular disk of thickness d, radius R, and density p. The disk is free to rotate about a pivot at its inertially fixed center O. An a x 4a xd rectangular slot is cut into the disk, and a rectangular solid piston, which is modeled as a block constrained by a pure and ideal spring of spring constant k, slides without friction in the slot. The piston has mass m and dimensions a xaxt where t is the thickness in the Z direction. The spring is unstretched when x = 0. The unstretched spring length is 3a/2. Reference frame oxyz is inertial and reference frame oxıyız, is attached to the disk. Derive the equations of motion using Lagrange's Equations. R M