The transfer function of a linear system is defined as the ratio of the Laplace transform of the output function y(t) to the Laplace transform of the input function g(t), when all initial conditions are zero. If a linear system is governed by the differential equation below, Y(s) for this system. use the linearity property of the Laplace transform and Theorem 5 to determine the transfer function H(s) = G(s) y'' (t) + 8y' (t) +9y(t) = g(t). t> 0 Click here to view Theorem 5 H(s) = Let f(t) f'(t)... -1) (t) be continuous on [0,∞) and let f(n) (t) be piecewise continous on [0,00), with all these functions of exponential order a. Then for s> a, the following equation holds true. L {f{")} (s) = s^L{f}(s) — s"~1¹f(0) -sª-²f'(0) --- (-¹) (0)