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lap = InverseLaplaceTransform[(12*183.26)/((s^2 + 183.26^2) (55* s^2 + (5.5*s^2 (s*24.2525 + 784.243))/ (5.5*s^2 + 24.2525*s + 784.243) + 8000)), s, t]; {re, im} = (Simplify[#@lap, Assumptions -> t ∈ Reals] // ComplexExpand // Chop) & /@ {Re, Im}; re (* 0.0000328276 E^(-0.675566 t) Cos[10.5332 t] - 0.0000164059 E^(-1.74968 t) ...



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