How to get the critically damped vibration equation

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    Damped Vibration

how to u get the critically damped equation

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

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

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

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zina
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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)
 
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