I am attempting the question shown in the attachment. It can be seen that the poles are located at -2 ± 3j which expressed in terms of s is (s + 2)2 + 32. This is the denominator, but how is the numerator of the transfer function found? Edit: Looking at the Laplace look-up table I would want the numerator to be 3 giving: 3/((s + 2)2 + 32) so that i could use e-atcosωt to perform the reverse Laplace transform in part b. Is this correct?