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Trouble with harmonic oscillator equation

  1. Oct 9, 2013 #1
    Consider the harmonic oscillator equation (with m=1),
    x''+bx'+kx=0
    where b≥0 and k>0. Identify the regions in the relevant portion of the bk-plane where the corresponding system has similar phase portraits.

    I'm not sure exactly where to start with this one. Any ideas?
     
  2. jcsd
  3. Oct 10, 2013 #2

    jfizzix

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    there are certain regions of b and k where the oscillator will undergo overdamped motion, underdamped motion, and critically damped motion. The phase space trajectories of overdamped motion look a lot different than those of underdamped motion. Solving the equation of motion should tell you which values of b and k correspond to which kinds of motion. I expect this is what is being asked.
     
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