A ball of mass 'm' is inside of a tube that rotates in a horizontal plane around the vertical axis (Drawing a circunference). Attached to the ball (inside of the tube) there is a massless, inextensible rope that goes to the midpoint of the circle described by the rotating tube. The other end of the rope is attached to a hanging block of mass 'M'. Describe the motion of the ball in terms of its position as a function of time. 2. Relevant equations My non inercial reference system was x parallel to the tube, z perpendicular to the plane (in the opposite direction of the hanging block) and y in the plane but perpendicular to x. After solving the dynamics of the problem, the differential I got (I think it is correct) was: m * w2 * x - M*g = (m+M) * x'' where w is the angular speed of the tube and x is the position of the ball along the tube starting from the center of the circumference described by it. x'' is the acceleration of the ball along the tube, which is the same of the acceleration of the hanging block. Of course, the first term is the centrifugal force and the second one is the weight of the block. 3. The attempt at a solution Now my problem is the next one. When solving this differential (proposing for the homogeneous solution: A * eL*t , and for the particular solution x''=0) I only got a solution where x increases exponential with time, but what about the other case, in which the hanging block is heavier and x decreases with time? Thanks!