Question

16. 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 -C1 C1 LC2-C2 with ci k/mi for i1, 2. Show that the eigenvalues of the coefficient matrix A are λ 1 = 0 and λ2 =-c1-c2. with associated eigenvectors V1 [ 1 1 ]1 and V2 = [ c1 -c2] C1 -C2 x'(0) = 0 x2"(0) = 0 xj(t) r2(t) FIGURE 5.4.13. The two railway cars of Problems 16 through 19.

Answer 1

Civc 2 2- C 2X2 2 x 2

=D and 2 be tha eijeuvec 2 2. 2. 2 2. and