Re: A Question About A Simple LRC circuit

["John S. Denker" <jsd@MONMOUTH.COM>]

At 04:33 PM 3/5/01 -0500, Robert B Zannelli wrote:
> instantaneous ...... a step voltage
> input with a theoretical dv/dt=infinity to simplify the question.

Ho ho ho!  If you want to go down that road, there is a type of input even
more instantaneous than a step function, namely a delta function.

It turns out that it is tremennnndously useful to know how a linear system
responds to a delta-function excitation.  (This includes RC, LC, and RLC
circuits, masses on springs, and about ten jillion other things.)

Question:  How does a damped harmonic oscillator respond to a
delta-function excitation?

Hint:  You already know the answer.
Hint:  What happens if you hit a bell with a hammer?

Answer:  The response is zero for all times t<0.  Thereafter it is a damped
sine wave.

This is illustrated at
 http://www.monmouth.com/~jsd/physics/rlc-green.gif

=================

In case you were wondering why this is so useful:  Any function can be
represented as a sum of delta functions.  Therefore, for a linear system,
the response to any excitation whatsoever (!) can be represented as a sum
of these response-to-delta-function-excitation curves.