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Problem 3. The black semi-circular surface is stationary. The blue disk of mass m and radius R rolls without slipping on the black surface. The disk is attached to a spring at its center. The red slot allows the spring to move freely in the vertical direction and does not interfere with the motion ofthe disk. The unstretched length ofthe spring is R. [3] Determine the equation of motion of the disk in terms of 6. (b) Determine the natural frequency of unforced vibrations of the disk for small excursions about its equilibrium position