Help finding inverse laplace transform?

t_n_k

Joined Mar 6, 2009
5,448
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.
 

t_n_k

Joined Mar 6, 2009
5,448
BTW - I believe you have the signs mixed up for k1 & k2

k1=2
k2=-4
 
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