Help finding inverse laplace transform?


Joined Mar 6, 2009
One approach would be to replace k1 & k2 with their known values and reform X(s) as the 'simple' ratio of two polynomials with k3 & k4 included in the numerator polynomial.

You could then for instance evaluate X(0) by setting s=0, thereby giving a value for the known X(s) and also a value for the numerator containing the unknowns k3 & K4.

Alternatively one could take s as one or both of the real roots of the known numerator polynomial 9s^2-15s-104=9(s+8/3)(s-13/3) for which the function X(s) then evaluates to zero. The equivalent numerator polynomial with unknowns k3 & k4 would also evaluate to zero for either of those roots.

In any case you could form two algebraic expressions in k3 & K4 from which those unknowns could then be found.

If you are up to the task, you could ignore the hint & evaluate the residues for the two complex conjugate poles.