Bead on rod
A small bead of mass m is free to slide on a thin rod. r ω m The rod rotates in a plane about one end at constant angular velocity ω. Show that the motion is given by r = Ae-γt + Be+γt , where γ is a constant which you must find and A and B are arbitrary constants. Neglect gravity. Show that for a particular choice of initial conditions [that is, r(t = 0) and v(t = 0)] it is possible to obtain a solution such that r decreases continually in time, but that for any other choice r will eventually increase. (Exclude cases where the bead hits the origin.)
