A 6-kg uniform cylinder is assumed to roll without sliding on a horizontal surface and is attached

Question:

A 6-kg uniform cylinder is assumed to roll without sliding on a horizontal surface and is attached by a pin at point C to the 4-kg horizontal bar AB. The bar is attached to two springs, each of constant k = 3.5kN/m as shown. Knowing that the coefficient of static friction between the cylinder and the surface is 0.5, determine the maximum amplitude of the motion of point C which is compatible with the assumption of rolling.