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Simple Harmonic Problem 2

  1. Dec 13, 2012 #1
    Hi friends the problem is -

    https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/30370_2656498989013_1471109032_n.jpg

    Attempt -

    friends as per the question I am trying to get the acceleration- displacement equation for this problem. So I am using

    F = - (dU / dx)
    Differentiating Potential energy function w.r.t. x I get,

    F = - (2a + 4b .x3)

    But F = mass. acceleration so,

    acceleration = - (2a/m + 4b/m x3)

    Now I am sticking here that how to proceed further to get the result like,

    acceleration = - ω2 . x

    Please friends help me in solving this Problem.

    Thank you all in advance.
     
  2. jcsd
  3. Dec 13, 2012 #2

    TSny

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    Check to make sure that you took the derivative of ax2 correctly. Also keep in mind that you are considering "small" oscillations.
     
  4. Dec 14, 2012 #3
    F = - (dU / dx)
    Differentiating Potential energy function w.r.t. x I get,

    F = - (2ax + 4b .x3)

    But F = mass. acceleration so,

    acceleration = - (2a/m.x + 4b/m x3)

    It is for small oscillations so x3 will be neglected.

    Hence accn = -(2a/m).x

    acceleration = - ω2 . x

    hence The answer comes, ω = √(2a/m)

    Yet the answer is not achieved. In the book the answer is option (B)
     
  5. Dec 14, 2012 #4

    TSny

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    I think you got the right answer. I don't see how (B) could be the answer.
     
  6. Dec 14, 2012 #5
    Yes there is mistake in the answer of book.
     
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