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Prove the lorentzian function describes resonant behavior

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data

    Resonances occur in many physical systems, and are often observed by measuring the frequency response of the system to an applied driving force. use the example of a damped harmonic oscillator to show how the lorentzian function serves as a good description of resonant behavior


    2. Relevant equations

    [itex]P_{L}( x; \mu ,\Gamma)[/itex] = [itex]\frac{\Gamma/2}{\pi(x-\mu)^{2} +( \Gamma/2)^{2} }[/itex]

    cb343dcde6b56c7005578467c51c2049.png

    3. The attempt at a solution

    this is for an honours lab, and the "lecture" part isn't taught well at all. So i kind of need help to start this problem
     
  2. jcsd
  3. Sep 27, 2011 #2
    anyone got an idea? and something happend to my initial equations...
     
  4. Sep 27, 2011 #3

    vela

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    You want to add a forcing term F(t) that drives the oscillator, so your equation becomes
    [tex]m\ddot{x} = F(t) -kx -c\dot{x}[/tex]Use something like F(t)=A sin ωt and find the particular solution to the differential equation.
     
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