In the figure S_(1) and S_(2) are two light springs of stiffness k and 4k respectively. When springs are in relaxed state, seperation between their free ends is 2x_(0) . A uniform solid cylinder of mass m and radius R( lt x_(0)) is placed exactly midway between the free ends of the springs with its axis horizontal and perpendicular to the springs . Now consider the two cases separately. Case I : The cylinder is imparted speed v_(0) towards left. When the cylinder comes to rest momentarily the co-ordinates of its centre are either (-x_(1), R) or (x_(2),R) . Case II: The Cylinder is imparted speed v_(0) toward left and angular speed omega^(0) in clockwise sense simultaneously . At the time of maximum compression in the springs the co-ordinates of centre of the cylinder are either (-x_(3),R) " or "(x_(4),R) Now answer the following questions assuming that friction is absent every where. Choose the correct option