QUESTION 1 &(t) => HE 1- Find the differential equation of the system above. Use f(t)...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. a. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer. 2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t)...
Use the differential equation approach to find Vo(t) for t> 0 in the circuit in the figure below 1k0 Please round all numbers to 3 significant digits. Vo(t)
3. Consider the differential equation ty" - (t+1)yy = te2, t> 0. ert is a solution to the corresponding homogeneous (a) Find a value of r for which y = differential equation (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation
Chapter 7, Problem 7.014 Use the differential equation approach to find it) for t>0 in the circuit in the figure below. 1 H t=0 iL(t) 3 V 12Ω 6Ω 6Ω 3Ω Please round all numbers to 3 significant digits. Click here to enter or edit your answer L(t) ok
7.13 Use the differential equation approach to find v.(t) for t > 0 in the network in Fig. P7.13. 4H TO + 1 = 0 2013 342 340 0.(t)
Question given an LTI system, characterized by the differential equation d’y() + 3 dy + 2y(t) = dr where x(t) is the input, and y(t) is the output of the system. a. Using the Fourier transform properties find the Frequency response of the system Hw). [3 Marks] b. Using the Fourier transform and assuming initial rest conditions, find the output y(t) for the input x(t) = e-u(t). [4 Marks] Bonus Question 3 Marks A given linear time invariant system turns...
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
Problem 1. The input x(t) and output y(t) of an LTI system satisfy the differential equation d’y(t) + wốy(t)=r(t), where wo is a fixed real number. A) Find the right-going impulse response of the system. B) Find the left-going impulse response of the system.
Problem # 1 For each system Derive the differential equation which describes the system. Use Laplace Trans form to find the Transfer Function. Specify the number of the Poles and Zeros and the value of the Gain. Determine the system's order both based on the Transfer Function and the number of the energy storage elements. Draw the Block Diagram with Input and Output C. Liquid Level System; assume q is the input and h3 is the output ! Ay Ry...
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...