A cricket pitch roller consists of a circular cylinder of mass 110 kg and radius m is connected to the back of a tractor by two springs, r one on each side of the roller and each of stiffness , as shown in the figure. When the tractor stops the system is observed to vibrate k with a period of 2 s. The motion is purely aligned in the direction of the axis. x Using the energy method and assuming that the cylinder is free to roll on the rough horizontal grass surface without slipping, that there is negligible damping in the system, and that the tractor is effectively a rigid system as it is much stiffer than the spring, calculate the stiffness of each spring in ____________ N/m.

x m