1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Equilibrium of Forces on a Spring

  1. Jun 15, 2009 #1
    1. The problem statement, all variables and given/known data

    A particle of mass M moves in one dimension along the positive x axis, under the influence of two forces. The first force is a constant force, with magnitude B and direction toward the origin. The second force is an inverse square law, with magnitude A/x2 and direction away from the origin.

    [Data: M = 0.30 kg; B = 14 N; A = 34 Nm2.]

    2. Relevant equations

    Find the potential energy function, and sketch the energy diagram for motion with kinetic energy K. Find the equilibrium position.
    Calculate the frequency of small oscillations around the equilibrium.

    3. The attempt at a solution

    I first set Fnet = ma = -B + A/x2

    1st: Am I correct to say the resorting force (toward the origin) is - ?

    if so, I then rearranged the problem to look like a differential:

    m*x[tex]^{''}[/tex] + B = A/x2

    divide by m, and multiply by x2,

    x2*x[tex]^{''}[/tex] + B*x2/m = A/m

    Is the set-up correct? or do I need a velocity term in here? Thanks for any help, or criticism as to how to write my questions better.
  2. jcsd
  3. Jun 16, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi alexander_i! :wink:
    Yes, that's the force …

    but now answer the question

    what is the potential energy function? :smile:
  4. Jun 16, 2009 #3
    Thanks for the reply!

    We know dU(x) = F*dx,

    and I did set up and energy equation before

    E = -(1/2)*k*x2 + (1/2)*m*v2 - fr*x

    and when I take the derivative, I of course get back to my Fnet.

    Am I trying to solve this differential? or did I not pick up on your question?
  5. Jun 16, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    ok, so what is U?

    and what is the relation between U and K?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook