Harmonic vibrations of board on movable rolls

On movable rolls lies board. Board's mass is m1. Board's length is l. Rollers has equal mass m2. Rollers execute rotary motion which rotational velocity is ω. Rollers are rotating in opposite directions. Between board's surface and rolls is kinetic sliding friction which is described by sliding friction factor ƒ. When board was in equilibrium position its center of gravity was in the middle of distance between rolls centers. Next board was perticipated from equilibrium position by Δx distance. After precipitation from equilibrium position board executes harmonic vibrations. Subject of example is to find harmonic vibration period. We assume that there is no energy dissipation.