Solving Part c of Repulsive Force Homework Problem

[physics148]

Homework Statement

(2) Suppose a particle of mass m is subjected to a repulsive force F = +kx.
(a) What is the general solution for the motion of the system?
(b) If the particle begins with a position x(0) = x0 and with velocity v(0) = v0 at t = 0 what are the values of the constants appearing in the general solution?
(c) There is a solution where the particle starts at x0 and moves toward the origin only to remain
at rest there. What is the initial velocity v0?.

Homework Equations

[/B]

The Attempt at a Solution

So I solved part a) and b) and got (what I believe is the right answer) of
a) x(t)=C1e^(wt)+C2e^(-wt)
b)x(t)=(wx0+v0)e^(wt)/(2w)+(wx0-v0)e^(-wt)/(2w)

for part c, how would I go about solving it? I initiallly thought of equating velocity and position, since they are both equal when the particle is at rest, but I think I should instead somehow incorporate force, since the velocity will have to be negative to combat the positive repulsive force, but I'm uncertain on how to obtain v0.

 

[kuruman]

Find an expression for the velocity as a function of time. Then you want to find at what v₀ that expression goes to zero as time becomes very large.

 

[physics148]

awesome. figured it out by taking the limit. thanks!