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[DPRG] RE: Critically Damped?

Subject: [DPRG] RE: Critically Damped?
From: Lance Rose LRose at pilgrimspride.com
Date: Wed May 28 12:20:01 CDT 2003

I respectfully request that all future post be posted in english (or with an
english translation). ;)

I think I understood about 4 words of this one...

> My ancient circuits book reminded me that the roots of the 
> characteristic
> equation determine the dampedness of the system (in this case, an RLC
> circuit, since it doesn't contain any "zeros", only "poles"  
> The "poles"
> determine the stability of the system, if I remember 
> correctly).  Terrible,
> long-suppressed nightmares of Bode plots and frequency 
> response diagrams
> re-entered my consciousness.  Anyhow, there are three 
> possible solutions:
> 
> 1) The roots may be real and distinct, if the square of the 
> radian frequency is greater than the square of the neper 
> frequency.  The
> system is then underdamped.
> 
> 3) The roots may be real and equal, if the square of the 
> resonant radian
> frequency is equal to the square of the neper frequency.  The 
> system is then
> critically damped.
> 
> 
> A square wave passing through an underdamped circuit can "ring", or
> oscillate appreciably before settling.  An overdamped 
> circuit's output can
> approach the final value asymptotically, and perhaps never 
> quite reach it.
> (Depending on how underdamped or overdamped the circuit is).
> 
> Here's my question...I seem to recall an interesting bit of 
> arcane trivia
> about a critically damped system, perhaps related to the 90% 
> settling time
> or the area under the curve or something.  Can anyone enlighten?

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