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(3 points) Given the system 1. -2 0 2i and for the eigenvalue λ-2, the vector V-(1) is an eigenvector. we know that...
plesse show work 11. For the system dr 1 1 -3 -5 31 Y , initial...
plesse show work
11. For the system dr 1 1 -3 -5 31 Y , initial condition Y, - (4,0) Write the solution and sketch the x(i) and y(1) graphs of the particular solution If the eigenvalues are of the form a + ib, b0 then determine if the origin is a spiral sink, a spiral source, or a center determine the natural period and natural frequency of of the oscillations determine the directions of the oscillations in the phase...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general...
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general solution. b) State if the origin is a spiral sink, or a source, or a center. c) Write the natural period and the natural frequency of the solutions. d) Do the solutions go clockwise or anti clockwise around the origin? (0) e) Write the particular solution that corresponds to ly(0) =
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Dete...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral s...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y,
Problem 3. For the...
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c)...
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution dY (1 -2
For the system: a. Write the general solution b. State if the origin is a spiral...
For the system:
a. Write the general solution
b. State if the origin is a spiral sink, source, or center and
explain why.
c. Write the natural period and natural frequency of the
solutions.
d. Do the solutions go clockwise or anticlockwise around the
origin? Explain your reasoning.
e. Write the particular solution that corresponds to
Please write clearly and explain your steps. Thank you! Do not
just copy someone else's answer.
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector...
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
(1 point) 2. Find the most general real-valued solution to the linear system of diferential equations...
(1 point) 2. Find the most general real-valued solution to the linear system of diferential equations 7' = [4 4]z. x1 (1) -2iexp(-4t)exp(-21" 2i*exp(-4t)exp(21*t = C1 + C2 x2 (1) exp(-4t)exp(-21) exp(-4t)exp(2i*t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses O spiral source O spiral sink
(1 point) a. Find the most general real-valued solution to the linear system of differential equations...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
plesse show work
11. For the system dr 1 1 -3 -5 31 Y , initial condition Y, - (4,0) Write the solution and sketch the x(i) and y(1) graphs of the particular solution If the eigenvalues are of the form a + ib, b0 then determine if the origin is a spiral sink, a spiral source, or a center determine the natural period and natural frequency of of the oscillations determine the directions of the oscillations in the phase...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general solution. b) State if the origin is a spiral sink, or a source, or a center. c) Write the natural period and the natural frequency of the solutions. d) Do the solutions go clockwise or anti clockwise around the origin? (0) e) Write the particular solution that corresponds to ly(0) =
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y,
Problem 3. For the...
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution dY (1 -2
For the system:
a. Write the general solution
b. State if the origin is a spiral sink, source, or center and
explain why.
c. Write the natural period and natural frequency of the
solutions.
d. Do the solutions go clockwise or anticlockwise around the
origin? Explain your reasoning.
e. Write the particular solution that corresponds to
Please write clearly and explain your steps. Thank you! Do not
just copy someone else's answer.
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
(1 point) 2. Find the most general real-valued solution to the linear system of diferential equations 7' = [4 4]z. x1 (1) -2iexp(-4t)exp(-21" 2i*exp(-4t)exp(21*t = C1 + C2 x2 (1) exp(-4t)exp(-21) exp(-4t)exp(2i*t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses O spiral source O spiral sink
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
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