A system of differential equations can be created for two masses connected by springs between one another, andconnected to opposing walls. The dependent variables form a 4 × 1 vector y consisting of the displacement andvelocity of each of the two masses. For the system y' = Ay, the matrix A is given by:00100001-3715 -8 015 -37 0 -8Because the system oscillates, there will be complex eigenvalues. Find the eigenvalue associated with thefollowing eigenvector.-6i6i36 + 24i-36 - 24i

Answered: Image /qna-images/answer/673454c1-3df1-4c39-88da-2218e8322c79.jpg

Answered: A system of differential equations can…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Consider the initial value problem 0 - 1 x+ 2t ㅇ *(0): Form the complementary solution to the homogeneous equation. x.(t) = a1 + a2 help (formulas) help atrices) Construct a particular solution by assuming the form x,(t) = äe21 + bt + č and solving for the undetermined constant vectors ā, b, and č. help (formulas) X,(t) = help (matrices) Form the general solution x(t) = x.(t) + x,(t) and impose the initial condition to obtain the solution of the initial value problem. |- X1(t) x2(t) help (formulas) help (matrices)
a.) Form the complimentary solution to the homogeneous equation. y_c(t) = c_1 [ _ _] + c_2 [ _ _] b.) Construct a particular solution by assuming the form y_P(t) = e^(-3t)a and solving for the undetermined constant vector a. y_P(t) = [ _ _] c.) Form the general solution y(t) = y_c(t) + y_P(t) and impose the initial condition to obtain the solution of the initial value problem. [y_1(t) y_2(t)] = [ _ _]
b) A system of differential equation is given as follows: x₁ = 9x₁ - 4x₂ x₂ = 8x₁ - 3x₂ where x₁ and X2 are functions of . Given that the eigenvalues of A= and 5 with the corresponding eigenvectors i) Write a matrix P that diagonalizes A. ii) Write a diagonal matrix D such that P¹ AP = D. iii) Hence, find the general solution to the system. [4=[83] are 1 and respectively.
Solve the system of differential equations given in matrix form for the general solution. We must do this by calculating the eigenvalues and eigenvectors. Note: we get a repeated eigenvalue and must solve for the second eigenvector to get two linearly independent solutions for our general solution. Please explain how you calculate the second eigenvector
Consider the system of ODEs: x' = -3x – y y' = 4x + 2y Find the equilibrium solution(s) and classify them based on the eigenvalues and eigenvectors of the associated coefficient matrix. You do NOT need to solve the system. Please type in your step-by-step solution.
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 5x+6y=0 y" - 5x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? O A. x₁ = x¹, x₂ =y' O B. X₁ =X, X₂=X', X3 = Y, X4=y' OC. x₁ = x, X₂=x", X3 = Y. X4=y" OD. x₁ = x¹, x₂ = x¹, x₂ =y', X4=y" Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. O B. X₁ X₂ x₁² X1 x2 x3 X4 X1
A system of ordinary differential equations has 2 x 2 state matrix with eigenvalues and corresponding eigenvectors (eigenpairs) A1 = 5, v1 = and A2 = -6, Based on the given eigenpairs write down the general solution to the associated system of differential equations. The solution must be written as a |¤1(t) single vector like a =
Consider the linear system dx₁ dt dx₂ dt = 4x1 - 3x₂ = 3x1 + 4x2. 1. Show that upon conversion to the form X'= AX, the eigenvalues of A are complex. 2. Find the general solution of the system.
Consider a system of differential equations which has the general solution: 18]- = C, · cos (5. t) – sin (5 - t) )+C2 · sin (5 - t) + • Cos (5 - t (a) Determine the fundamental matrix (t) which has the property (0) = I. (t) = (b) Use the fundamental matrix found in part (a) to quickly determine the particular solution for the following initial conditions: r (t) : y (t) = :8]-[- (0): 1 (ii) r (t) = y (t) =
Use Newton's method with the starting point (1,2)T to find a solution of the system +y 0 2+y = 1. The first iteration produces the vector (A) (2,2)T (B) (2,1) (C) (1,1)" (D) (1,2)" (E) none of the above O (A) O (B) O (C) O (D) O (E)
If A is an (n x n)-matrix of real constants that has a complex eigenvalue and eigenvector v, then the real and imaginary parts of w(t) = elty are linearly independent real-valued solutions of x' =Ax: x₁(t) = Re(w(t)) and X₂(t) = Im(w(t)), The matrix in the following system has complex eigenvalues; use the above theorem to find the general (real-valued) solution. 0 30 -3 0 0 X 005 x(t) = = x' = Find the particular solution given the initial conditions. x(t) = = x(0) = 123
Suppose the eigenvalues associated with a 2 by 2 matrix of a system of linear ODE's are complex conjugates. (a) Use Euler's formula to rewrite the solution in the form x(t) = u(t) + iv(t). (b) Show that x(t) = u(t) + v(t) is also a solution of the system.

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS