1. (a) Write the modified (generalized) node equations considering the initial conditions in s-domain for the circuit given below. (b) Express the equations in the matrix form. İL(0) vc(0) Voz=k2vc di d2 d3 İR1 †) J(t) R2 R1
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- If I have to break the question piecemeal, write how I should divide it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" "John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.), ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. Are the following systems linear? Is it memoryless? Is it causal? Explain your answer. Can impulse response and transfer function be found for systems? Find if it can be found, if not, explain why. (Note: The input of the system is "z(t)" and the output is "y(t)". “8{t)" is unit impulse, "1(t)" is unit step function. In some cases, impulse response or transfer function is already given In this case, find what is not given if it can be found.) 7. System with transfer function G(s) = 8. System with transfer function G(s) =…PartI S, Give the symbolic expression for the emf E using KVL for the circuit with S1 closed and Sz open. Give your answer in terms of the current I, resistor R, capacitors C1 and Cz and charges stored in the respective capacitors Q, and Q2. Use * to denote product and / to denote division. So to group the product of, say, a and b_1 write a b_1. And to write a ratio of say, c_1 and d write C_1/d. To add the product and ratio write a*b_1 + c_1/d. a)Write the mathematical expression for emf E. E= 29 kN, two capacitors C1 = 3.3 µF and C2 = 4.4 µF and In the figure there's a circuit with an emf E = 19 V, two resistors R1 = 22 kl and R2 two switches S and Sz. b) Find the time constant for this configuration of the circuit. Time constant T Give your answer up to at least three significance digits. ms c) Find how much charge will be stored in C2 after time t = 0.9T seconds. Charge stored in C2 Give your answer up to at least three significance digits. PartII After t = 10r seconds, we open…If I have to break the question piecemeal, write how I should divide it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" "John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.), ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. Are the following systems linear? Is it memoryless? Is it causal? Explain your answer. Can impulse response and transfer function be found for systems? Find if it can be found, if not, explain why. (Note: The input of the system is "z(t)" and the output is "y(t)". “8{t)" is unit impulse, "1(t)" is unit step function. In some cases, impulse response or transfer function is already given In this case, find what is not given if it can be found.) 7. System with transfer function G(s) = 8. System with transfer function G(s) =…
- If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: “Chi Tsong Chen, Linear System Theory and Design" "John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.),ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. 1. Are the systems whose input-output relationship is given as below linear? Is it memoryless? Is it causal? Does it change over time? Find transfer function and impulse responses if available, explain why not. (ult) indicates the input of the system, y(t) the output. 6(t) is a unit impulse, 1(t) is a unit step function.) e. y(t) = 1(t) f. y(t) = 0in steady state space model matrix b can be used to: a. configure the output.b. facilitate a throughput of the input to the output.c. characterize the dynamic response d. none of the aboveIf I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" “John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots,Etc.), ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions,ExplainThemWithTheirReasons. Are the systems whose input-output relationship is given as below linear? Is it memoryless? Is it causal? Does it change over time? Find transfer function and impulse responses if available, explain why not. (u(t) indicates the input of the system, y(t) the output. 8(t) is a unit impulse, 1(t) is a unit step function.) а. у(t) %3D b. y(t) = cos(3t) u(t) и(t - 2) + u(2 - t) = Sje-t+wu(w)dw d. y(t) = S u(w)dw e. у(t) %3D 1(t) f. y(t) = 0 с. у(t) %3D -2t I| %3D
- If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" “John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.),ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions,ExplainThemWithTheirReasons. 1. The input of the adjacent circuit is “u(t) = V1(t)" and its outputs are "yı (t) = ig1(t)" (current on R1) İR1, and "y2 (t) = V11 (t)" (Voltage on L1). R1 L1 C1 a) Obtain the state space representation of the system for "x, (t) = Vca(t)" and "x2 (t) = i1(t)". b) (in parameters) c) Obtain the state space representation of the system for the state variables ;(t) = 2ig1 (t) + V11 (t) and K2(t): = 3 ) dt. (in parameters) d) For "R1 = 1, C1 = 1, L1 = 1", find the transfer function matrix of the system separately from the…If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" “John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots,Etc.),ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. 3. Consider the circuit given below. The inputs are Is1 and Is2 currents, the outputs are VC1 and VC2 voltages. C2 C1 + VC2 - + VCI ILI L1 Is1(1) Vs1 R1 R2 S VR2 (1IS2 VR1 а. Let the state variables be VC1, VC2, İL1 respectively. Write the state space representation of the system. (It will be written in terms of parameters. If not, explain why.)If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" “John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.),ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. 1. The input of the adjacent circuit is "u(t) = V1(t)" and its outputs are "yı (t) = ir1(t)" (current on R1) İR1, and "y2 (t) = V11 (t)" (Voltage on L1). R1 L1 C1 a) Obtain the state space representation of the system for "x, (t) = Vc1(t)" and “x2 (t) = i1(t)". b) (in parameters) c) Obtain the state space representation of the system for the state variables *1(t) = 2i1(t) + V11 (t) and 2(t) = 3dt) (in parameters)
- If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: “Chi Tsong Chen, Linear System Theory and Design" "John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.), ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. 3. Consider the circuit given below. The inputs are Is1 and Is2 currents, the outputs are VC1 and VC2 voltages. C2 C1 + VC2 - + VC1 iL1 L1 Is1(1 vs1 R1 R2: 1Is2 VR1 VR2 a. Let the state variables be VC1, VC2, iL1 respectively. Write the state space representation of the system. (It will be written in terms of parameters. If not, explain why.) b. Get the transfer function matrix of the system using the state space representation you found in part "a". (It will be written in terms of parameters. It must be done using…If I have to ask the question piece by piece, write down how I should ask it. Subject : "Lineer Algebra"(ElectricalEngineering) Books about the question: "Chi Tsong Chen, Linear System Theory and Design" “John S. Bay, Fundamentals of Linear State Space Systems" NOTE:ACalculatorOrComputerCanBeUsedForNumericalCalculations(MatrixMultiplication,Polynom- ialRoots, Etc.), ButTheQuestionsCannotBeSolvedByTheComputer.SomeQuestionsMayNotHaveSolut- ions, ExplainThemWithTheirReasons. 1. Are the systems whose input-output relationship is given as below linear? Is it memoryless? Is it causal? Does it change over time? Find transfer function and impulse responses if available, explain why not. (ult) indicates the input of the system, y(t) the output. 6(t) is a unit impulse, 1(t) is a unit step function.) b. у(t) %3D cos(3t) u(t) c. y(t) = f, e-t+wu(w)dwGraph the inverse CTFTs of the functions in Figure