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Math Help - resonance involing an ODE

  1. #1
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    resonance involing an ODE

    Hi

    my question is

    For the ODE below, write down the forcing function f(t)that will lead to resonant behaviour (t\rightarrow\infty). Verify your choice by calculating the particular intergral that corresponds to your forcing and examining its limit as t\rightarrow\infty<br />
    a) y^{(4)}+5\ddot{y}+4y=f(t)

    my solution to y^{(4)}+5\ddot{y}+4y=0 is y_{c}=Asin(x)+Bcos(x)+Csin(2x)+Dcos(2x)

    thanks
    Last edited by cooltowns; March 20th 2010 at 12:45 PM.
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  2. #2
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    Quote Originally Posted by cooltowns View Post
    Hi

    my question is

    For the ODE below, write down the forcing function f(t)that will lead to resonant behaviour (t\rightarrow\infty). Verify your choice by calculating the particular intergral that corresponds to your forcing and examining its limit as t\rightarrow\infty<br />
    a) y^{(4)}+5\ddot{y}+4y=f(t)

    my solution to y^{(4)}+5\ddot{y}+4y=0 is y_{c}=Asin(x)+Bcos(x)+Csin(2x)+Dcos(2x)

    thanks
    Ya - if you force your system with an f(t) that contains any member of the complimentary solution it will resonant {\it i.e.} if f(t) = \sin t the solution will contain a terms like t \sin t and t \cos t.
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