Consider the differential equations below, where x(t) is the input variable and y(t) the output variable....

 

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Consider the differential equations below, where x(t) is the input variable and y(t) the output variable. dy(t) + 2y(t): = dt 2 d³y(t) + dt³ 7 d'y(t) dt² 5x(t) + 3 +3 +21 dy(t) dt + 9y(t) 3x(t) Determine for each equation: i) Laplace Transfer function. ii) The Transfer Function (TF) G(s) by using appropriate change of variable. Explain why you must use a change of variable. iii) Determine the stability of each TF G(s) 1 of 3 iv) Draw unit step and impulse responses of each TF (In the midterm you may be asked to sketch i.e. rough drawing of similar TF or Using Matlab). No inverse of Y(s) is requested. v) Use the final value theorem to get y(t) at steady state conditions. Consider the differential equations below, where x(t) is the input variable and y(t) the output variable. dy(t) + 2y(t): = dt 2 d³y(t) + dt³ 7 d'y(t) dt² 5x(t) + 3 +3 +21 dy(t) dt + 9y(t) 3x(t) Determine for each equation: i) Laplace Transfer function. ii) The Transfer Function (TF) G(s) by using appropriate change of variable. Explain why you must use a change of variable. iii) Determine the stability of each TF G(s) 1 of 3 iv) Draw unit step and impulse responses of each TF (In the midterm you may be asked to sketch i.e. rough drawing of similar TF or Using Matlab). No inverse of Y(s) is requested. v) Use the final value theorem to get y(t) at steady state conditions.

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To solve the given differential equations we need to follow a systematic approach i Laplace Transfer ... View the full answer