The figure shows two railway cars with a buffer spring. We want to investigate the transfer of momentum that occurs after car 1 with initial velocity v0 impacts car 2 at rest. The differential equation is given below. Show that the eigenvalues of the coefficient matrix A are λ1=0 and λ2=−c1−c2, with associated eigenvectors v1= 1 1 T and v2= c1 −c2 T. x′′= −c1 c1 c2 −c2 x with ci=k /mi for i=1, 2

The figure shows two railway cars with a buffer spring. We want to investigate the transfer of momentum that occurs after car 1 with initial velocity v0 impacts car 2 at rest. The differential equation is given below. Show that the eigenvalues of the coefficient matrix A are λ1=0 and λ2=−c1−c2, with associated eigenvectors v1= 1 1 T and v2= c1 −c2 T. x′′= −c1 c1 c2 −c2 x with ci=k /mi for i=1, 2

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.17P

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