1. Not finding help here? Sign up for a free 30min 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!

How to find if equilibrium points of a force is un/stable?

  1. Apr 7, 2016 #1
    1. The problem statement, all variables and given/known data
    U = Ax2 - Bx3

    2. Relevant equations
    du/dx = 2Ax - 3Bx2

    3. The attempt at a solution

    If I was given a potential energy function U = Ax2 - Bx3 and am asked to find:

    1) The expression for the force as a function of x.

    2) The equilibrium points and determine if are they stable or unstable?

    So, for 1):
    Would I differential the function giving like so?

    U' = f'(x) = 2Ax - 3Bx2

    Now for 2):
    Would I set f'(x) = 0 to find the equilibrium points?

    f'(x) = 2Ax - 3Bx2 = 0

    In return I get the points of x through the quadratic equation:
    x = 0 and X = A/B

    If this is all correct how can I determine if a equilibrium point is stable or unstable?
     
  2. jcsd
  3. Apr 7, 2016 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Recall the force is negative derivative of the potential energy.
    X=0 is correct, but you have a mistake in the other equilibrium point.

    The equilibrium is stable if the potential energy is minimum in that point and unstable if it is maximum.
     
  4. Apr 7, 2016 #3
    Oh sorry, x = 2A/(3B).
    How I find the max and min of potential energy?
     
  5. Apr 7, 2016 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You found the positions of the extremes, at x=0 and at x=2A/3B.
    Have you learnt what should be the second derivative at a maximum and at a minimum?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How to find if equilibrium points of a force is un/stable?
  1. Stable equilibrium (Replies: 3)

Loading...