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, use the linearity property of the Laplace Y(s) transform and Theorem 5 to determine the transfer function H(s) = = G(s) system. y''(t) + 3y' (t) + 5y(t) = g(t), t> 0 Click here to view Theorem 5. H(s) = for this

Determine the values of r for which the given differential equation has solutions of the form y = e't. Give the answers in ascending order. y"-6y" + 8y = 0 r = r = r = Jud L IN

Let f be a function on R with Fourier transform 1 F[f](s) = f(s) = f(x) e** dx. irs (a) Show that the Fourier transform of the function ga(x) : f(ax), where a > 0 is a constant, is Flg.|(6) = Lf (). 1 (b) Show that the Fourier transform of the function Je-, r20 f(x) = 0, x < 0 is f(s) = 1 1+ is V2n s2 +1