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Asymmetrical Linear Spring

  1. Sep 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider an asymmetrical nonlinear spring whose force law is given by F=-kx+(k2)x^2 + (k3)x^3.


    Here's the problem statement as a google doc:


    2. Relevant equations
    U=integral (F,dx)
    3. The attempt at a solution

    a. It's called an asymmetrical spring because the force necessary to stretch the spring x units changes depending on how far the spring is from the origin. So basically, graphically, the force by distance graph looks like x^3, which is NOT symmetric about the y axis, thus the spring is asymmeetrical.

    b. So, for this I thought what I could do was find the potential energy at the original distance of .5 meters. I would do this by integrating Fdx. Thus, U(.5)=16.66666
    Now, I find U(.25), which is: U(.25)=6.7708333. Thus, KE=U(.5))-U(.25)=9.896

    Thus, 9.896=mv^2/2, and m=2 kg, so I can solve for v using that equation, which would give me:

    v=3.14157 m/s

    Is that right?
  2. jcsd
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