Physics · Rotational Motion

A uniform cylinder of mass M and radius R is attached to two identical massless springs (spring constant k) fixed to a wall. The springs are connected symmetrically to a axle passing through the cylinder, each at a distance d from the cylinder's center. The system lies in a horizontal plane. The cylinder rolls without slipping on the surface. When the center of mass is displaced by x from its equilibrium position, the net restoration force acting on the center of mass can be written as F = -Mω2x. If the acceleration of the center of mass is a = -(α•k/M)x, what is the effective constant α for pure rolling?