Question

A solid uniform cylinder of mass m performs small oscillations due to the action of two springs whose combined stiffness is equal to x (Fig. 4.18). Find the ** of these oscillations in the absence of sliding.

Answer 1

Let k1 and k2 be the spring constant o f left and right sides springs. As the rolling of the solid cylinder is pure its lowest point becomes the instanteneous centre of rotation. If θ be the small angular displacement of its upper most point relative to its equilibrium position, the deformation of each spring becomes (2R θ) . Since the mechanical energy of oscillation of the solid cylinder is conserved, E = T+ U = constant