![18. Given the electric network shown in Figure P1.6. Review] a. Write the differential equation for the network if v(t)- u(t), a unit step. b. Solve the differential equation for the current, i(t), if there is no initial energy in the network. c. Make a plot of your solution if R/L 1 i (t) FIGURE P1.6 RL network](http://img.homeworklib.com/questions/9b100a30-c3cd-11ea-8c12-e1f3f0c6d1bb.png?x-oss-process=image/resize,w_560)
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![fo icti= ist is = 1 | b [l-e-t] ucts so plot of ا م ( 0, 632 - - - * حد](http://img.homeworklib.com/questions/9c67b310-c3cd-11ea-99e1-01bf8367855c.png?x-oss-process=image/resize,w_560)
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18. Given the electric network shown in Figure P1.6. Review] a. Write the differential equation for...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE)...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE) for the capacitor voltage. Find the zero-state unit step responses of v(t) and i(t) if vs-u(t) V using each of the following three methods of solving the ODE: a. b. i. ii. Solve the ODE by integrating for the solution; Solve the ODE by assuming homogeneous and particular solutions; Solve the ODE by using the general form solution for a 1st order ODE. iii....
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, ho...
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibi...
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibits stable oscillatory behavior. Van der Pol realized the parallel between the oscillations generated by this equation and certain biological rhythms, such as the heartbeat, and proposed this as a model of an oscillatory cardiac pacemaker. Solve the van der Pol equation using Second-order Runge Kutta Heun's method with the...
It shows that the electric circuit shown in the figure is described by the system of differential equations. Where x1 is...
It shows that the electric circuit shown in the figure
is described by the system of differential equations. Where x1 is
the current that will pass through the coil, x2 is the voltage drop
in the capacitor, and I (t) is the current produced by the external
source
Explain your procedure
L 8 henrys I(t) Cfarad R= 4 ohms 7-4 ohms 18 12 5
L 8 henrys I(t) Cfarad R= 4 ohms 7-4 ohms
18 12 5
P 4.38 12 of 18 > Review Consider the circuit shown in (Figure 1). Sketch i(t)...
P 4.38 12 of 18 > Review Consider the circuit shown in (Figure 1). Sketch i(t) to scale versus time. Plot the points for the values of t that are separated by the step Al = 0.28 No elements selected iz(t) (A) Figure 1 of 1 > -0 R = 10 + D + 02 04 06 08 10
Solve the following differential equation using MATLAB's ODE45 function. Assume that the all init...
Solve the following differential equation using MATLAB's ODE45 function. Assume that the all initial conditions are zero and that the input to the system, /(t), is a unit step The output of interest is x dt dt dt To make use of the ODE45 function for this problem, the equation should be expressed in state variable form as shown below Solve the original differential equation for the highest derivative dt 2 dt Assign the following state variables dt dt Express...
write MATLAB scripts to solve differential equations. Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle...
write MATLAB scripts to solve differential equations.
Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
1-) Write your solution on a paper and please write your name and ID on the...
1-) Write your solution on a paper and please write your name and ID on the paper 2-) Scan your solution as a single pdf file (your scan should be clearly readable and aligned well) 3-) Then you can upload your solution and make sure that you upload your file within the time allocated for the question. Late submissions will not be accepted!!!! 4-) Unless otherwise stated by the instructor, DO NOT EMAIL your solution Consider the electrical circuit shown...
What is the solution for this first order nonlinear differential equation of this SIR model with...
What is the solution for this first order nonlinear differential equation of this SIR model with these initial conditions? S(t)=not infected individuals (1) l(t)- Currently Infected (588) R(t)- recovered individuals (0) This will be a nonlinear first order differential equation(ODE) dasi d/dt-sal-kt di/dt a (s-k/a) i dr/dt-ki Total population will be modeled by this equation consistent with the SlR model. d(S+l+R)/dt= -saltsal-kltkl-0 Solution: i stk/aln stK Model the topic using a differential equation. a) Draw any visuals (diagrams) that exemplify...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE) for the capacitor voltage. Find the zero-state unit step responses of v(t) and i(t) if vs-u(t) V using each of the following three methods of solving the ODE: a. b. i. ii. Solve the ODE by integrating for the solution; Solve the ODE by assuming homogeneous and particular solutions; Solve the ODE by using the general form solution for a 1st order ODE. iii....
' 1. Review Question a) Name three applications for feedback control systems. b) Functionally, how do closed-loop systems differ from open-loop systems? c) Name the three major design criteria for control systems. d) Name the performance specification for first-order systems. e) Briefly describe how the zeros of the open-loop system affect the root locus and the transient response. What does the Routh-Hurwitz criterion tell us? f) 2. Given the electric network shown in Figure. a) Write the differential equation for...
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibits stable oscillatory behavior. Van der Pol realized the parallel between the oscillations generated by this equation and certain biological rhythms, such as the heartbeat, and proposed this as a model of an oscillatory cardiac pacemaker. Solve the van der Pol equation using Second-order Runge Kutta Heun's method with the...
It shows that the electric circuit shown in the figure
is described by the system of differential equations. Where x1 is
the current that will pass through the coil, x2 is the voltage drop
in the capacitor, and I (t) is the current produced by the external
source
Explain your procedure
L 8 henrys I(t) Cfarad R= 4 ohms 7-4 ohms 18 12 5
L 8 henrys I(t) Cfarad R= 4 ohms 7-4 ohms
18 12 5
P 4.38 12 of 18 > Review Consider the circuit shown in (Figure 1). Sketch i(t) to scale versus time. Plot the points for the values of t that are separated by the step Al = 0.28 No elements selected iz(t) (A) Figure 1 of 1 > -0 R = 10 + D + 02 04 06 08 10
Solve the following differential equation using MATLAB's ODE45 function. Assume that the all initial conditions are zero and that the input to the system, /(t), is a unit step The output of interest is x dt dt dt To make use of the ODE45 function for this problem, the equation should be expressed in state variable form as shown below Solve the original differential equation for the highest derivative dt 2 dt Assign the following state variables dt dt Express...
write MATLAB scripts to solve differential equations.
Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
1-) Write your solution on a paper and please write your name and ID on the paper 2-) Scan your solution as a single pdf file (your scan should be clearly readable and aligned well) 3-) Then you can upload your solution and make sure that you upload your file within the time allocated for the question. Late submissions will not be accepted!!!! 4-) Unless otherwise stated by the instructor, DO NOT EMAIL your solution Consider the electrical circuit shown...
What is the solution for this first order nonlinear differential equation of this SIR model with these initial conditions? S(t)=not infected individuals (1) l(t)- Currently Infected (588) R(t)- recovered individuals (0) This will be a nonlinear first order differential equation(ODE) dasi d/dt-sal-kt di/dt a (s-k/a) i dr/dt-ki Total population will be modeled by this equation consistent with the SlR model. d(S+l+R)/dt= -saltsal-kltkl-0 Solution: i stk/aln stK Model the topic using a differential equation. a) Draw any visuals (diagrams) that exemplify...
2.7. Consider the differential equation for the RC circuit in Fig. P.2.12: Figure P. 2.12 R=1 r(t) =tu(t) C=1/4F y(t) (b) dy(t)dt+4y(t)=4x(t) Let the input signal be a unit step, that is, x(t) = u(1). Using the first-order differential equation solution technique discussed in Section 2.5.1 find the solution y(t) for t2 0 subject to each initial condition specified below: a. y (O) = 0 b. y (O) = 5 c. y (0) = 1 d. y (0) = -1...
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