1. Not finding help here? Sign up for a free 30min 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!

Nonhomogeneous: Undetermined coefficients

  1. Apr 30, 2005 #1
    (d^2x/dt^2)+(w^2)x=Fsin(wt), x(0)=0,x'(0)=0

    Hope that's readable. First part is second derivative of x with respect to t. w is a constant and F is a constant. I need to find a solution to this using method of undetermined coeffecients and I'm confused with all the different variables. Anyone get me started at least?
     
  2. jcsd
  3. Apr 30, 2005 #2

    Pyrrhus

    User Avatar
    Homework Helper

    Well, first off start by solving the homogenous equation to find the fundamental solution.

    [tex] \ddot{x} + \omega^{2}x = 0 [/tex]

    After that try a Particular solution of the type

    [tex] y_{p} = A x \sin(\omega t) + B x\cos(\omega t) [/tex]

    Remember that if the fundamental solution has already sin and cos, you will need to try a xsin and xcos, like this case.
     
    Last edited: Apr 30, 2005
  4. Apr 30, 2005 #3
    I got my homogenous equation x''+(w^2)x=0 but I can't find my roots with that w^2 in there.
     
  5. Apr 30, 2005 #4

    Pyrrhus

    User Avatar
    Homework Helper

    What seems to be the problem? Show me your work.
     
  6. Apr 30, 2005 #5

    Pyrrhus

    User Avatar
    Homework Helper

    Here, i will start you off

    [tex] \ddot{x} + \omega^{2}x = 0 [/tex]

    we assume a as a solution

    [tex] x(t) = e^{rt} [/tex]

    So we substitute in our ODE

    [tex] r^{2}e^{rt} + \omega^{2}e^{rt} = 0 [/tex]

    so

    [tex] e^{rt}(r^{2} + \omega^{2}) = 0 [/tex]

    because [itex] e^{rt} [/itex] cannot be equal to 0

    [tex] r^{2} + \omega^{2} = 0 [/tex]

    which ends up as

    [tex] r = \pm \omega i [/tex]
     
    Last edited: Apr 30, 2005
  7. May 1, 2005 #6
    I figured it out, thanks a lot for your help, I was just being dumb.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Nonhomogeneous: Undetermined coefficients
Loading...