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Real and Simple or Distinct Poles
If all the poles of F1(s) are of first order, Equation may be written in terms of a partial fraction expansion as
where p1, p2,..., pn are distinct, and K1, K2,..., Kn are nonzero finite constants. For any k, the evaluation of the residue Kk of F1(s) corresponding to the pole s = pk is done by multiplying both sides by (s - pk) and letting s → pk,
Equation is valid for k = 1, 2, . . . , n. Once the K's are determined in Equation, the inverse Laplace transform of each of the terms can be written easily in order to obtain the complete time solution.
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