1. Use the power method to determine the largest eigenvalue and corresponding eigenvector for this matrix. 8 10 8 4- 5 10 5 [2-2 7-1 Then, repeat this problem to determine the smallest eigenvalue and its corresponding eigenvector. Derive the set of differential equations for a three mass-four spring system as shown in Figure below that descrībes their time motion. Write the three differential equations in matrix form (Acceleration vector} + [k/m matrix] (displacement vector x} = 0 Note each equation has been divided by the mass. Solve for the eigenvalues and natural frequencies using Faddeev-Leverier Method and Power method for the following values of mass and spring constants kị = k, = 15 N/m, k: = kɔ = 35 N/m, and mị = m; = m3 = 1.5kg. Assume initial value for power method. Compare the relative error between these two methods. 2.
1. Use the power method to determine the largest eigenvalue and corresponding eigenvector for this matrix. 8 10 8 4- 5 10 5 [2-2 7-1 Then, repeat this problem to determine the smallest eigenvalue and its corresponding eigenvector. Derive the set of differential equations for a three mass-four spring system as shown in Figure below that descrībes their time motion. Write the three differential equations in matrix form (Acceleration vector} + [k/m matrix] (displacement vector x} = 0 Note each equation has been divided by the mass. Solve for the eigenvalues and natural frequencies using Faddeev-Leverier Method and Power method for the following values of mass and spring constants kị = k, = 15 N/m, k: = kɔ = 35 N/m, and mị = m; = m3 = 1.5kg. Assume initial value for power method. Compare the relative error between these two methods. 2.
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![Use the power method to determine the largest eigenvalue and corresponding
eigenvector for this matrix.
1.
[2-A
8 4-A
8
10
5
10
5
7-1]
Then, repeat this problem to determine the smallest eigenvalue and its corresponding
eigenvector.
2.
Derive the set of differential equations for a three mass-four spring system as shown in
Figure below that describes their time motion. Write the three differential equations in
matrix form
{Acceleration vector} + [k/m matrix]
{displacement vector x} = 0
ll
m
m2
ll
m3
Note each equation has been divided by the mass. Solve for the eigenvalues and natural
frequencies using Faddeev-Leverier Method and Power method for the following
values of mass and spring constants kị = k4 = 15 N/m, k: = ks = 35 N/m, and mị = m;:
= m3 = 1.5kg. Assume initial value for power method. Compare the relative error
between these two methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F427021d6-48d9-4aa7-a791-3ed5910e2dea%2F0d78d3ba-29ef-4c9d-b80a-c5472dafe8f9%2Fwum70e_processed.png&w=3840&q=75)
Transcribed Image Text:Use the power method to determine the largest eigenvalue and corresponding
eigenvector for this matrix.
1.
[2-A
8 4-A
8
10
5
10
5
7-1]
Then, repeat this problem to determine the smallest eigenvalue and its corresponding
eigenvector.
2.
Derive the set of differential equations for a three mass-four spring system as shown in
Figure below that describes their time motion. Write the three differential equations in
matrix form
{Acceleration vector} + [k/m matrix]
{displacement vector x} = 0
ll
m
m2
ll
m3
Note each equation has been divided by the mass. Solve for the eigenvalues and natural
frequencies using Faddeev-Leverier Method and Power method for the following
values of mass and spring constants kị = k4 = 15 N/m, k: = ks = 35 N/m, and mị = m;:
= m3 = 1.5kg. Assume initial value for power method. Compare the relative error
between these two methods.
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