Question 2: Perform the inverse Laplace transform of the following rational fractions using partial fraction expansion. List the procedures and verify the results with the MATLAB function \"ilaplace\". Attach the MATLAB codes and results. (1) $F(s) = \frac{s+1}{(s^2+2s+2)^2}$ (2) $F(s) = \frac{s^2+s+1}{(s+2)(s^2+2s+1)}$ (10 marks) (10 marks)
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For the first rational fraction, we have: F(s) = (s^2 + 25 + 2)^2 / (s^2 + 5 + 1) To perform partial fraction expansion, we need to factorize the denominator: s^2 + 5 + 1 = (s + 1)(s + 5) Now we can write the rational fraction as: F(s) = A / (s + 1) + B / (s + Show more…
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a) Evaluate the Laplace transform of the following functions: i. f(t) = sin 2t + cos t ii. f(t) = t^3 + e^-2t iii. f(t) = te^-2t + t b) Express (2s+2)/(s^2+5s+6) in partial fraction form and then find the inverse Laplace transform of (2s+2)/(s^2+5s+6) using the partial fraction obtained.
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Problem 2: Expand the following function F(s) into partial fractions using MATLAB. Determine the inverse Laplace transform of F(s). F(s) = 1 / (s^4 + 5s^3 + 7s^2) The MATLAB program for determining the partial-fraction expansion is given below: Problem 3: For the following function F(s): F(s) = (s^4 + 3s^3 + 5s^2 + 7s + 25) / (s^4 + 5s^3 + 20s^2 + 40s + 45) Using MATLAB, find the partial-fraction expansion of F(s). Also, find the inverse Laplace transformation of F(s). Problem 4: Find the Laplace transform of the following function using MATLAB. f(t) = 7t^3 cos (5t + 60°) f(t) = -7te^-5t f(t) = -3 cos 5t Problem 5: Determine the inverse Laplace transform of the following functions using MATLAB. F(s) = s / (s(s + 2)(s + 6)) F(s) = (3s + 1) / (s^2 + 2s + 9)
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