- #1

physics148

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## 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

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## 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.