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Re: TC Differential Equations
Tesla List wrote:
>
> Original Poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
>
> Tesla List wrote:
>
> > What do you mean by "The coefficients of the common Laplace
> transform
> > denominator"? I'm not familiar with this nomenclature, and am curious
> > about it.
>
> I listed the coefficients for the numerators of Vc1(s), Vc2(s), Il1(s),
> and
> Il2(s). All have the same denominator D(s). For example, using the first
> two
> polynomials in my message:
>
> n3 s^3 + n2 s^2 + n1 s + n0
> Vc1(s) = Vc1(0) --------------------------------------
> d4 s^4 + d3 s^3 + d2 s^2 + d1 s + d0
>
> To obtain Vc1(t), expand this expression in partial fractions, what will
> usually result in two real terms, and apply the inverse Laplace
> transform
> to them, what results in two sinusoids multiplied by exponential
> decaying
> factors. The Teslasim program lists the final expressions.
>
> > (Of course, my last course in Laplace transforms was in the
> > spring of 1948, and I'm sure the world of circuit analysis has advanced
> > since then.)
>
> Not much in this area.
>
> Antonio Carlos M. de Queiroz
Antonio:
Finally figured out what you meant by those coefficients when I took a
good look at the expressions which represented them. Hadn't ever run
across that notation before.
Thanks,
Ed