1. The problem statement, all variables and given/known data An overdamped oscillator with natural frequency w and damping coefficient y starts out at a position xo>0. What is the maximum initial speed (directed toward the origin) it can have and not cross the origin? 2. Relevant equations Overdamped Case Equation x(t)=Ae^(-(y-ohm)t) + Be^(-(y+ohm)t) 3. The attempt at a solution Differentiating the above equation, simplifying, differentiating again and setting it to 0 and solving to t(max)....but I get stuck here with a really complicated equation. I'm not sure how to solve for A and B given the initial condition of xo>0. Can someone set me in the right direction?