# Repulsive force

Tags:
1. Nov 5, 2016

### physics148

1. The problem statement, all variables and given/known data
(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?.
2. Relevant equations

3. 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.

2. Nov 5, 2016

### 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.

Last edited: Nov 5, 2016
3. Nov 7, 2016

### physics148

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