Maximum Initial Speed of an Overdamped Oscillator

[TheRedDragon]

Homework Statement

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?

Homework Equations

Overdamped Case Equation

x(t)=Ae^(-(y-ohm)t) + Be^(-(y+ohm)t)

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?

 

[clamtrox]

What you should probably do first is to solve A and B in terms of y, w, x₀ and v₀. Once you have them, just plug them into the formula for x(t), then find when x(t) = 0 and solve v₀ from that.