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I want convert laplace function into partial fractions like k1/(s+s1) + k2/(s+s2)

asked 2018-04-17 10:17:39 -0500

I have a expression in 's' domain: I(s)= Ip.(s-A)/(s^2+Bs+C) I want to convert to partial fractions like: I(s)= k1/(s-s1) + k2/(s-s2) and finally use in time domain as: i(t)=k1.exp(s1.t-t0) + k2.exp(s2t-t0) thank you for your attention

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slelievre gravatar imageslelievre ( 2018-04-17 10:56:29 -0500 )edit

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answered 2018-04-17 12:29:21 -0500

Is this what you want?

sage: var('s')
sage: var('t')
sage: L = (s-3)/(s^2-3*s+2)
sage: L.partial_fraction()
2/(s - 1) - 1/(s - 2)
sage: L.inverse_laplace(s,t)
-e^(2*t) + 2*e^t
sage: L.partial_fraction().inverse_laplace(s,t)
-e^(2*t) + 2*e^t

Once you have an expression like L = (s-3)/(s^2-3*s+2), if you type L.<TAB>, it will produce a list of all of the available methods. In this case there are a lot of possibilities, but inverse_laplace and partial_fraction are two of them. (If you can guess that something like partial_fraction might be there, you can also type L.p<TAB> or<TAB> to get a much shorter list.) You can also evaluate L.inverse_laplace? to get documentation.

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Asked: 2018-04-17 10:17:39 -0500

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Last updated: Apr 17