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  • 4 years ago

Why is it said that critical damping leads to the fastest decay? If a system with amplitude 1 is slightly underdamped it crosses the x axis but it's absolute value is less than that of the system with critical damping up to f(x) ~ 10^-25. For the system: x''+cx'+x=0 critical damping (c=2) x=e^(-x)+x*e^(-x) underdamped (c=1.9, wd=sqrt(4-1.9^2)/2) x=e^(-x*b/2)*cos(wd*x)+(b/2/wd)*sin(wd*x) =e^(-x*1.9/2)*(cos(.39^.5/2*x)+(1.9/.39^.5)*sin(.39^.5/2*x))

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  1. anonymous
    • 4 years ago
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    I looked in a textbook and saw that the wording in the 18.03 lecture notes is not ideal. In the textbook the wording was "fastest decay without oscillation." I agree with this statement.

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