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Homework Help: Second order differential equation

  1. Mar 24, 2014 #1
    1. The problem statement, all variables and given/known data

    http://books.google.co.uk/books?id=...ilibrium length&pg=PA136#v=onepage&q&f=false

    2. Relevant equations

    All in the link.

    3. The attempt at a solution

    The solution is there, its to do with part (c), I would realy appreciate it if someone would explain how they make the jumps - especially to the second last equation
  2. jcsd
  3. Mar 24, 2014 #2


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    Science Advisor
    Homework Helper

    They used the Binomial theorem.
    $$\frac{1}{(d + \Delta d)^2} =\frac{1}{d^2}\left(1 + \frac{\Delta d}{d}\right)^{-2}
    = \frac{1}{d^2}\left(1 - 2\frac{\Delta d}{d} + \cdots\right)$$

    Everything before that looks like straightforward algebra. The last step to find ##\omega## is the standard solution of the differential equation for simple harmonic motion.
  4. Mar 24, 2014 #3
    Ignore- spotted mistake
    Last edited: Mar 24, 2014
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