1. Limited time only! Sign up for a free 30min personal 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!

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

    AlephZero

    User Avatar
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted