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A small bead of mass m is free to slide along a long, thin rod without any friction. The rod rotates in a horizontal plane about a vertical axis passing through its end at a constant rate of f revolutions per second. Show that the displacement of the bead as a function of time is given by r(t)=A1(e^bt) +A2(e^–bt) , where r is measured from the axis of rotation. Find the expression for the constant b. Also, how would you determine the constants A1 and A2?