Consider an LTI system whose impulse response h(t) is real, and whose associated system function is H(s). Suppose throughout this problem that the input is x(t) = e-3t cost, for all t, and that the corresponding output y(t) is well defined for this input.
(a) If you were allowed to determine the value of H(s) for only a single value of s, which value of s would you pick in order to obtain an explicit time-domain expression for the output y(t) corresponding to the above input? Now write down such an expression for y(t) in terms of H(s) evaluated at the s that you selected.
(b) Suppose it is known that y(0) = 0 and y?(0) = 1. Reduce your expression for y(t) in part (a) to the form y(t) = e-3t (Acost + B sin t), and determine the constants A and B.