1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Repulsive force

  1. Nov 5, 2016 #1
    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)

    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. jcsd
  3. Nov 5, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
  4. Nov 7, 2016 #3
    awesome. figured it out by taking the limit. thanks!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted