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Second order ODE into a system of first order ODEs

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  1. Mar 5, 2017 #1
    1. The problem statement, all variables and given/known data
    The harmonic oscillator's equation of motion is:

    x'' + 2βx' + ω02x = f

    with the forcing of the form f(t) = f0sin(ωt)


    3. The attempt at a solution

    So I got:
    X1 = x
    X1' = x' = X2
    X2 = x'
    X2' = x''
    ∴ X2' = -2βX2 - ω02X1 + sin(ωt)

    The function f(t) is making me doubt this answer because I have to take into account f0 and it just disappears in the solution.

    (For context I have to put it into a system of first order ODEs because I have to code it into python and plot the results with the given parameters.)

    Am I on the right track? Or am I missing anything?
     
  2. jcsd
  3. Mar 5, 2017 #2

    BvU

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    Looks to me you made it disappear in the equations already.
     
  4. Mar 5, 2017 #3
    Oh so I shouldn't have taken it out in the first place then? That makes sense thanks! Other than that, am I missing anything else?
     
  5. Mar 5, 2017 #4

    BvU

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    Initial conditions ?
     
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