Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Second order DE with Sine function

  1. Apr 7, 2017 #1
    I have this second order differential equation but I'm stumped as to how to solve this since the zeroth order term has a Sine function in it and the variable is embedded.

    ##\ddot y(t) + 3H (1+Q) \dot y(t) -m^2 f \sin(\frac{y(t)}{f}) = 0##

    ##H~##, ##~Q~##, ##~m~##, and ##~f~## are just constants.

    I even tried to use DSolve in mathematica but there is an error. How do I solve this? Can anyone guide me with this problem?
     
    Last edited: Apr 7, 2017
  2. jcsd
  3. Apr 7, 2017 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Google damped pendulum differential equation
    [edit] and there's always this
     
  4. Apr 8, 2017 #3
    Are you pertaining to the small angle approximation? I know that is a possibility but the problem is that ##\theta = \frac{y[t]}{f} \approx 1##.
     
  5. Apr 8, 2017 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Small angle is the first approach. The article in the link discusses the full equation in section 3.
     
  6. Apr 8, 2017 #5
    If you're interested in non-linear equations, I recommend this book which includes a step-by step solution of the non-linear pendulum:

    http://store.doverpublications.com/0486609715.html
     
  7. Apr 9, 2017 #6
    I still can't find the solution to my given equation, can you kindly give me a hint/note onto where I should look?
     
  8. Apr 9, 2017 #7
    I was referring to the equation ## y''=k\sin(y)##. That's not yours but if you first study how this one is solved exactly in terms of elliptic functions, then perhaps you can adapt the method to yours. It's been a while that I've studied it (using the book I quoted) and I no longer have the book and don't recall exactly how it's done.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Second order DE with Sine function
  1. Second order DE (Replies: 6)

  2. Second order linear DE (Replies: 3)

  3. DE of second order (Replies: 5)

Loading...