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1. Write the state-space equations for the system shown below ri (t) +2 (t) u (t) Figure 1: Syste...
(1 point) In this problem you will solve the differential equation or @() (1) Since P(a) 0 are not analytic at and 2()...
(1 point) In this problem you will solve the differential equation or @() (1) Since P(a) 0 are not analytic at and 2() is a singular point of the differential equation. Using Frobenius' Theorem, we must check that are both analytic a # 0. Since #P 2 and #2e(z) are analytic a # 0-0 is a regular singular point for the differential equation 28x2y® + 22,23, + 4y 0 From the result ol Frobenius Theorem, we may assume that 2822y"...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above difterential equation has a singular point at-0. If the singular point at -0 is a regular singular point, then a power series for the solution y) can be found using the Frobenius method. Show that z-0 is a regular singular point by caliculating p/a)- 2(2) Since both of these functions are analytic at -0...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimas. (a) The above differential equation has a singular point at z-0.I the singular point at z -0 is a regular singular point, then a power series for the solution ()can be found using the Frobenius method. Show that z-O is a regular singular point by calculating plz)-3 Since both of these functions are analytic at r -0...
2. Solve each of these ODEs using power series method expanded around Xo = 0. Find...
2. Solve each of these ODEs using power series method expanded around Xo = 0. Find the recurrence relation and use it to find the first FOUR terms in each of the two linearly independent solution. Express your answer in general form where possible (well, it is not always possible). (a) (25 marks) (x2 + 2)y” - xy + 4y = 2x - 1-47 Note: expressa in terms of power series. (b) 2x2y" + 3xy' + (2x - 1) =...
Consider the following differential equation Note: For each part below you must give your answers in terms of fract...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a snaar point at x 0 . It the singular point at x-0 is a regular singular point, then a power series for the solution y(x) can be lound using the Frobenius method. Show that x = 0 is a regular sigar point by calculating: xp(x) = y(x) = Since both...
Consider the following difterential equation Note: For each part below you must give your answers in terms of fractions...
Consider the following difterential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a singular point at z-0.I the singular point at z-0 is a regular singular point, then a power series for the solution y)can be found using the Frobenius method. Show that z-0is a regular singular point by calculating: zr(z) = 2g() Since both of these functions are analytic at z-0 the...
8. Write down the state space equation for the system shown below US) + 2 y(s)...
8. Write down the state space equation for the system shown below US) + 2 y(s) $+3 2 s(s+1) 9. Derive the state space equation for the system shown where the coefficients of the system matrix are in diagonal form and the elements of the control matrix are unity. U(S) 1 X2 $+2 X 3+1 X = y $+3 $+4 S
A state space linear system is shown below. Use Matlab to solve the following problems. Requirement...
A state space linear system is shown below. Use Matlab to solve the following problems. Requirement for project report: (1) Results; (2) Matlab code. dx1/dt=-x1(t)+u(t) dx2/dt=x1(t)-2x2(t)-x3(t)+3u(t) dx3/dt=-3x3(t) y(t)=-x1(t)+2x2(t)+x3(t)+u(t) (1) Assume the system has input u(t)=e-3t if t>t0 and zero initial state x(0)=[0;0;0]. Using the transition matrix obtained, compute the system’s output (analytical solution), and plot the output as a function of time (t within 0 to 10). (2) Using the function lsim to simulate the system’s output (analytical solution), and...
Conslder the following differentlal equatlon, Note: For each part below you must give your answers in terms ot f...
Conslder the following differentlal equatlon, Note: For each part below you must give your answers in terms ot fractions (as appropriate), not decimals. (a) The above ditferential equation has a singular point at0. If the singular point at-0 is a regular singular point, then a power series for the solution y) can be found using the Frobenius method. Show that -0 is a regular singular point by calculating pa)2 Since both of these functlons are analytlic at regular the singular...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
(1 point) In this problem you will solve the differential equation or @() (1) Since P(a) 0 are not analytic at and 2() is a singular point of the differential equation. Using Frobenius' Theorem, we must check that are both analytic a # 0. Since #P 2 and #2e(z) are analytic a # 0-0 is a regular singular point for the differential equation 28x2y® + 22,23, + 4y 0 From the result ol Frobenius Theorem, we may assume that 2822y"...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above difterential equation has a singular point at-0. If the singular point at -0 is a regular singular point, then a power series for the solution y) can be found using the Frobenius method. Show that z-0 is a regular singular point by caliculating p/a)- 2(2) Since both of these functions are analytic at -0...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimas. (a) The above differential equation has a singular point at z-0.I the singular point at z -0 is a regular singular point, then a power series for the solution ()can be found using the Frobenius method. Show that z-O is a regular singular point by calculating plz)-3 Since both of these functions are analytic at r -0...
2. Solve each of these ODEs using power series method expanded around Xo = 0. Find the recurrence relation and use it to find the first FOUR terms in each of the two linearly independent solution. Express your answer in general form where possible (well, it is not always possible). (a) (25 marks) (x2 + 2)y” - xy + 4y = 2x - 1-47 Note: expressa in terms of power series. (b) 2x2y" + 3xy' + (2x - 1) =...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a snaar point at x 0 . It the singular point at x-0 is a regular singular point, then a power series for the solution y(x) can be lound using the Frobenius method. Show that x = 0 is a regular sigar point by calculating: xp(x) = y(x) = Since both...
Consider the following difterential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a singular point at z-0.I the singular point at z-0 is a regular singular point, then a power series for the solution y)can be found using the Frobenius method. Show that z-0is a regular singular point by calculating: zr(z) = 2g() Since both of these functions are analytic at z-0 the...
8. Write down the state space equation for the system shown below US) + 2 y(s) $+3 2 s(s+1) 9. Derive the state space equation for the system shown where the coefficients of the system matrix are in diagonal form and the elements of the control matrix are unity. U(S) 1 X2 $+2 X 3+1 X = y $+3 $+4 S
Conslder the following differentlal equatlon, Note: For each part below you must give your answers in terms ot fractions (as appropriate), not decimals. (a) The above ditferential equation has a singular point at0. If the singular point at-0 is a regular singular point, then a power series for the solution y) can be found using the Frobenius method. Show that -0 is a regular singular point by calculating pa)2 Since both of these functlons are analytlic at regular the singular...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
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