(Oscillating platform) A uniform horizontal platform of mass m is supported by counter-rot...

(Oscillating platform) A uniform horizontal platform of mass m is supported by counter-rotating cylinders a dis­tance L apart (see figure). The friction force f exerted on the platform by each cylinder is proportional to the normal force N between the

platform and the cylinder, with constant of pro­portionality (coefficient of sliding friction) µ; f = µN. Show that if the cylinder is disturbed from its equilibrium position (x = 0), then it will undergo a lateral oscillation of frequency , where g is the acceleration of gravity. HINT: Derive the equation of motion governing the lateral dis­placement x of the midpoint of the platform relative to a point midway between the cylinders.