Figure 5.4.13 shows two railway cars with a buffer spring. We want to investigate the transfer of momentum that oc- curs after car 1 with initial velocity vo impacts car 2 at rest. The analog of Eq. (18) in the text is x" -C1 C1 C2 -c2 with c; = k/m; for i = 1, 2. Show that the eigenvalues of the coefficient matrix A are 11 = 0 and 12 = -c1- c2, with associated eigenvectors Vị = [1 1]' and v2 = [c1 -c2]". -C2 xj'(0) = 0 x2'(0) = 0 k тi т2 oo.0.0 o0..O1 FIGURE 5.4.13. The two railway cars of

Figure 5.4.13 shows two railway cars with a buffer spring. We want to investigate the transfer of momentum that oc- curs after car 1 with initial velocity vo impacts car 2 at rest. The analog of Eq. (18) in the text is x" -C1 C1 C2 -c2 with c; = k/m; for i = 1, 2. Show that the eigenvalues of the coefficient matrix A are 11 = 0 and 12 = -c1- c2, with associated eigenvectors Vị = [1 1]' and v2 = [c1 -c2]". -C2 xj'(0) = 0 x2'(0) = 0 k тi т2 oo.0.0 o0..O1 FIGURE 5.4.13. The two railway cars of

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Solve the Matrix problem.

Figure 5.4.13 shows two railway cars with a buffer spring.
We want to investigate the transfer of momentum that oc-
curs after car 1 with initial velocity vo impacts car 2 at
rest. The analog of Eq. (18) in the text is
x"
-C1
C1
C2
-c2
with c; = k/m; for i = 1, 2. Show that the eigenvalues
of the coefficient matrix A are 11 = 0 and 12 = -c1- c2,
with associated eigenvectors Vị =
[1 1]' and v2 =
[c1 -c2]".
-C2
xj'(0) = 0
x2'(0) = 0
k
тi
т2
oo.0.0 o0..O1
FIGURE 5.4.13.
The two railway cars of

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