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How to get the critically damped vibration equation

  1. x(t)=e^(-wt) [x(0)(1+wt)+ dx/dt(0)t]

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  2. x(t)= e^-jwt [(9dx/dt (0) +x(0)jw')/w']sinw't +x(0) cos w't

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  3. j is the xi (greek alphabet which equals C/Cc and w' damping

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Multiple votes are allowed.
  1. Apr 24, 2009 #1
    1. SDOF Systems Governing Equation m(dx^2/dt^2) + c(dx/dt)+ kx = F(t)

    how do i get this equation below?

    Free Critically damped Vibration x(t) = e^(wt) [x(0)(1+wt) + (dx/dt)(0) t]

    (dx/dt is x with 1 dash on top)
     
  2. jcsd
  3. Apr 24, 2009 #2
    without the 9
     
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