Given the following differential equation of a causal system д?уду ac at2 - 6y(t) at at 7 where x(t) = u(t), with initia

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Given the following differential equation of a causal system д?уду ac at2 - 6y(t) at at 7 where x(t) = u(t), with initial conditions y(0) = 0, y'0) = -6. (a) (4 marks) Give the Laplace transform Y (3) of the signal y(t). (b) (4 marks) Compute the signal y(t) by inverse Laplace transform. Y(s) (c) (6 marks) Define H(s) = x® as the Laplace transform of system response. Give the expres- sion of H(s) and the corresponding system realization by Direct Form II. (d) (6 marks) Consider g(t) = Ohaft + ah(t) and its Laplace transform G(s), where a is a real constant. Determine the range of a such that the zero-point of G(s) is located in its Region of Convergence (ROC).