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!

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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook