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Help with Godstein Chapter 3

  1. Dec 11, 2013 #1
    This is a question to those who have the 3rd edition at their disposal. Where do 3.45 and 3.46 come from? I understood everything he said before that...
     
  2. jcsd
  3. Dec 12, 2013 #2
    Start with equ. 3.34, an linearize it about ##u = u_0##. You will get an equation for simple harmonic motion, from which those two equations will follow.
     
  4. Dec 12, 2013 #3
    I get an equation of the form x''+kx=c. where c is some constant, '' gives the second derivative with respect to theta, and x is u-u0.
     
  5. Dec 12, 2013 #4
    You are on the right track, but you should have obtained ##x'' + kx = 0##. You made a mistake somewhere. Without seeing your work, I can't say what it was.
     
  6. Dec 12, 2013 #5
    My work is attached.
     

    Attached Files:

  7. Dec 12, 2013 #6
    That u0^3 and u0 terms bother me, as you can see.
     
  8. Dec 13, 2013 #7
    The very first equation you have is incorrect. $$ {d \over du} V \left( \frac 1 u \right) \ne f(u) $$ Which is actually strange, because the third equation could only have been obtained if you had differentiated that correctly.
     
  9. Dec 13, 2013 #8
    OK, I get that now, thanks. I got the correct equation now. Now to get (3.46).
     
  10. Dec 13, 2013 #9
    3.46 should follow from what you got immediately: ##\ddot x + \beta^2 x = 0 ##.
     
  11. Dec 14, 2013 #10
    Yes. Thanks for the help with 3.45
     
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