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Can anyone solve this integral for spring mass oscillation?

  1. Feb 21, 2016 #1
    1. The problem statement, all variables and given/known data

    Capture.PNG

    So this is the question I need to solve. I was told to directly integrate the bottom equation to solve for x(t). I can solve (1) by differentiating (1) to turn it into 2nd order difffeq (mx''=kx), but I think I'm not allowed to do that ... I have no idea how to solve (2) using direct integration. It looks like a difficult non-linear equation to solve to me. please help me T T
    2. Relevant equations


    3. The attempt at a solution
    I solved (1) by turning into mx''=kx, but I'm not allowed to do that.
     
  2. jcsd
  3. Feb 21, 2016 #2

    TSny

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    Welcome to PF!

    Equation (2) is in terms of the two variables x and t. The ideas is to "separate" the two variables so that just the x variable occurs on one side and the t variable on the other, in such a way that the equation "begs" you to integrate both sides.
     
  4. Feb 21, 2016 #3
    Thank you! but then how do I integrate 1/(a-b*x^2)^(1/2) dx?
     
  5. Feb 22, 2016 #4

    TSny

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  6. Feb 22, 2016 #5
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