Consider the differential equation: +4+122= = 20t, r(0) -1,2(0) = 0 (a) (15 points) find its...

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Consider the differential equation: +4+122= = 20t, r(0) -1,2(0) = 0 (a) (15 points) find its solution without using Laplace transform. (b) (15 points) find its solution using Laplace transform. (1) (c) (5 points) Assume that the differential equation (1) represents a system model. For this system, if z is the output and 20t is the input, then under what conditions can you find the transfer function for this system? Under these assumptions, find the transfer function. (d) (5 points) Plot the pole/s and zero/s of the transfer function obtained in part (c). Is this system stable? Justify your answer. Consider the differential equation: +4+122= = 20t, r(0) -1,2(0) = 0 (a) (15 points) find its solution without using Laplace transform. (b) (15 points) find its solution using Laplace transform. (1) (c) (5 points) Assume that the differential equation (1) represents a system model. For this system, if z is the output and 20t is the input, then under what conditions can you find the transfer function for this system? Under these assumptions, find the transfer function. (d) (5 points) Plot the pole/s and zero/s of the transfer function obtained in part (c). Is this system stable? Justify your answer.