Two identical rollers are mounted with their axes parallel, in a horizontal plane, a distance $2$d$=31\mathrm{.}52$d$=31\mathrm{.}5$cm apart. The two rollers are rotating inwardly at the top with the same angular speed$$$0$$0.$ A long uniform board is laid across them in a direction perpendicular to their axes. The board of mass m$=3\mathrm{.}52$m$=3\mathrm{.}52$kg is originally placed so that its center of mass lies a distance x$0=10$x$0=10$cm from the point midway between the rollers. The coefficient of friction between the board and rollers is k$=0\mathrm{.}653$k$=0\mathrm{.}653.$ What is the period of the motion?