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Trace-determinant plane: underdamped systems

  1. Dec 8, 2009 #1
    1. The problem statement, all variables and given/known data

    Describe the set of points on the trace-determinant plane that describe all underdamped systems with period 2

    2. Relevant equations

    A harmonic oscillator can be represented by the equation m[tex]\frac{d^{2}y}{dt^{2}}[/tex] +b[tex]\frac{dy}{dt}[/tex]+ky=0 the Trace=-b/m and the Determinant=k/m.

    For an underdamped oscillator, the period is 4m[tex]\pi[/tex]/[tex]\sqrt{4km-b^{2}}[/tex]
    and T[tex]^{2}[/tex]-4D

    3. The attempt at a solution

    I have been trying to solve the equation 4m[tex]\pi[/tex]/[tex]\sqrt{4km-b^{2}}[/tex]=2 and then find T and D, but no luck really. I think the answer is all the points above a certain parabola.
  2. jcsd
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