Uh need to solve only (question 6) solve the q6 in one hour and get thumb up plz plz plz solve perfectly and handwritien soloution needed plz I also attached the answers of q3 I need perfect soloution according to question requirements plz Answer of Q:2S+ast2> Flt) = *sint PAnsAnswer of ONo:3%3D-tecost-xSintē cost -- ē'sint> Ans The charge on a capacitor g(t) in a circuit with a resistor, a capacitor and an inductor connectedin series driven by a given time-dependent voltage v(t) is governed by the second-order ODE"(t) + 20(t) +2q(t) = v(t).(1)A schematic of the RLC circuit can be found in the course notes..In Questions 1 - 6 you will calculate Laplace transforms / inverse Laplace transforms of fune-tions. These calculations will be useful in determining the response of (1) for an initial valueproblem specified in Question 7.You MUST use the method of solution as per the instructions found in each of the belowquestions.1 1. Use the linearity of property of Laplace transforms and the table of Laplace transforms onMyUni to find the Laplace transform ofv(t) = av (t) + Buy (t),where n (t) = 6(t – 2) and ty(t) = u(t – 3). Here, a and 8 are constants, and 6(t) and u(t)are the Dirac delta function and unit step function.2 2. Complete the square of the denominator and use the s-shifting theorem to find the inverseLaplace transform of the functionF(e) = 7 +2 +2Where applicable, you may use entries (1) through to (15) and the basic general formulaefrom the table of Laplace transforms on MyUni. You must NOT use any entries (16)through to (23).5 3. Use partial fraction decomponition, linearity and s-shifting theorem to find the inverseLaplace transform of the function1H(s) =s(s + 28 + 2)Where applicable, you may use entries (1) through to (15) and the basic general formulaefrom the table of Laplace transforms on MyUni. You must NOT use any entries (16)through to (23).4 4. Use the convolution theorem and your answer to Question 2 to verify the inverse Laplacetransform of the function H(s) found in Question 3. i.e. Find the inverse Laplace transformof the functionH(^) = »(² + 2» + 2) -F(0).1s(s² + 2s + 2)H(s) •You MUST evaluate the resulting integral by hand, and clearly show all your working.1 5. Use the t-shifting theorem and your answer to Question 2 to find the inverse Laplace trans-form of the functione-2K(s) =+28+2°1 6. Use the t-shifting theorem and your answer to Question 3 to find the inverse Laplace trans-form of the functionJ(s) =s(s +2s + 2)'4 7. Use Laplace transforms and the results from Questions 1 - 6 to find the response of (1)subject to the initial conditionsq(0) =0 and d'(0) = 1,with the time-dependent voltagev(t) = ab(t – 2) + Bu(t – 3).3 8. Plot the response, q(t), found in Question 7, on the interval 0

Answered: Image /qna-images/answer/0c44c9ea-546e-4c1b-a3fe-5d7023d94d25.jpg

Answered: J(s) = s(s +2s +2)

J(s) = s(s +2s +2)

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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