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Driven Damped Harmonic Oscillator, f != ma?

  1. Feb 26, 2007 #1
    Driven Damped Harmonic Oscillator, f != ma??

    Let's say I've got a driven damped harmonic oscillator described by the following equation:
    [tex]A \ddot{x} + B \dot{x} + C x = D f(t)[/tex]

    given that [tex] f = ma[/tex] why can't I write

    [tex]A \ddot{x} + B \dot{x} + C x = D ma[/tex]

    substitute [tex]\ddot{x} = a[/tex] to get

    [tex]A \ddot{x} + B \dot{x} + C x = D m \ddot{x}[/tex]

    and then rearrange to get

    [tex](A - D m) \ddot{x} + B \dot{x} + C x = 0[/tex]

    I know that's not how the problem is solved, but what is to stop me from solving it that way?
     
    Last edited: Feb 26, 2007
  2. jcsd
  3. Feb 26, 2007 #2
    Are you assuming constant acceleration?
     
  4. Feb 26, 2007 #3
    You're forgetting that f(t) is a time-varying force. You also have forces that depend on velocity and position, which is why what you wrote isn't correct. You only got the time-varying force.
     
  5. Feb 27, 2007 #4

    Meir Achuz

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    The F in Newton 's F=ma is the net force, which does not equal the function f(t) in your problem.
     
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