If I have a known square wave source, known capacitor value and known inductor value, what is the fastest way to figure out what the resistor value has to be to make the circuit overdamped, underdamped, and critically damped?

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    \$\begingroup\$ Online calculator. You want the damping factor to be 1 for critical damping. Enter your C and L and then try different R values until the damping factor is 1. Less than 1 is under-damped. More than 1 is over-damped. calctool.org/CALC/eng/electronics/RLC_circuit \$\endgroup\$ – mkeith Oct 25 '16 at 5:59
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    \$\begingroup\$ For a series RLC, critical damping is obtained when \$R=2\sqrt\frac{C}{L}\$. For underdamped, select lower \$R\$; for over-damped, select higher \$R\$. \$\endgroup\$ – Chu Oct 25 '16 at 8:44
  • \$\begingroup\$ So If I'm using a 100nF cap and a 100mH inductor in series, critical damping is when R = 0.02ohms only? If caps are usually smaller orders of magnitude than inductors does this make it difficult to get underdamping? \$\endgroup\$ – Austin Oct 25 '16 at 11:31
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    \$\begingroup\$ @Chu, wikipedia has a different equation. They say a = (R/2) * sqrt(C/L). Critical damping is when a=1. So that evaluates to R = 2 / sqrt(C/L). So for 100nF and 100mH, that works out to 2000 Ohms. Online calculator gives same result. This is for R in series. \$\endgroup\$ – mkeith Oct 25 '16 at 15:49
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    \$\begingroup\$ I got the L and C upside down. It's \$R=2\sqrt{\dfrac{L}{C}}\$ for series RLC with the output taken across C \$\endgroup\$ – Chu Oct 25 '16 at 16:06