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Kibble problem (linear motion chap. 2)

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data

    7. A particle of mass m moves (in the region x > 0) under a force F =
    −kx+c/x, where k and c are positive constants. Find the corresponding
    potential energy function. Determine the position of equilibrium, and
    the frequency of small oscillations about it.

    2. Relevant equations

    dx/dt = [(2/m)(E - V(x)]^1/2

    3. The attempt at a solution
    dx/[(2/m)(E+ Clnx - (1/2)kx^2]^1/2 = dt
    V = -Clnx + (1/2)kx^2]^1/2
    i think at equilibrum point V(x) must be zero but then how can i continue? This is en exam question and i must solve it completely correct. Thank you for your answers. (my firt language is not english. Sorry for mistakes.)
  2. jcsd
  3. Apr 18, 2010 #2


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    V(x) is not zero at equilibrium. What does equilibrium mean to you?
  4. Apr 18, 2010 #3
    Thanks, you are right. Total force, i think is zero at equilibrium point. So;
    -ka + [tex]\frac{c}{a}[/tex] = 0 (a = equilibrium point.) k = c/a2
    Is it true?
  5. Apr 18, 2010 #4


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    It is true. If this is an exam question, you have to finish it by yourself. I will not tell you how to solve it, but I can tell you if something is correct or not and the rest is up to you.
  6. Apr 18, 2010 #5
    The exam was three days ago. Nobody could solve this question and a similar one (in which F = -kx +a/x^3) The teacher gave us as a homework. If i will solve maybe my exam mark will increase but i am not sure this. Maybe not. If you don not want to help it is up to you. I will study on it again and again...
    Last edited: Apr 18, 2010
  7. Apr 18, 2010 #6
    I solved at last. a=(c/k)^1/2 and w=(2k/m)^1/2 , w=(V''(a) /m)^1/2. Thanks.
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