Given the following differential equation of a causal system дх Ә? уду at2 at - 6y(t) - at where x(t) = u(t), with initi

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Given the following differential equation of a causal system дх Ә? уду at2 at - 6y(t) - at where x(t) = u(t), with initial conditions y(0) = 0, y'(0) = -6. (a) (4 marks) Give the Laplace transform Y(s) of the signal y(t). (b) (4 marks) Compute the signal y(t) by inverse Laplace transform. 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. = = ah(t) (d) (6 marks) Consider g(t) at + 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).