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!

Homework Help: Driven oscillator ODE.

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data

    "The equation mx'' + kx = F0 * Sin (wt) governs the motion of an undamped harmonic oscillator driven by a sinusoidal force of angular frequency w. Show that the steady-state solution is

    x = F0 * Sin (wt) /(m * (w0^2 - w^2))

    2. Relevant equations

    x(t) = xta(t) + xtr(t) where xta = long term behavior and xtr = transient piece of solution

    xta(t) x0 cos (wt - (phi)

    where x0 = w0^2 X0/[(w0^2 - w^2)^2 + v^2*w^2]^1/2

    and phi = tan^-1(vw/(w0^2 - w^2)

    3. The attempt at a solution

    Honestly I'm not sure if the above equations are necessary. All my lecture notes tell me is that the long term behavior follows x0 * cos(wt - (phi)) so I'm not sure how I'm suppose to take that and turn it into F0 * Sin (wt) /(m * (w0^2 - w^2))

    I mean obviously I have a sin force driving my harmonic oscillator, but how do I use that to determine my long term solution?

    I really can't go much further than this at this point, I've been looking at this problem for a long time now and I can't scrap together anything useful.
  2. jcsd
  3. Sep 15, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    How about substituting this expression for x, and also the expression for x'', into the original differential equation?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook