EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 27, Problem 12P
Use the power method to determine the lowest eigenvalue and corresponding eigenvector for Prob. 27.10.
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Hello, could I get some help with a Differential Equations problem that involves Eigenvalues and Eigenvectors?
The set up is:
There are two toy rail cars, Car 1, and Car 2. Car 1 has a mass of 2 kg, and is traveling 3 m/s towards Car 2, which has a mass of 1 kg, and is traveling towards Car 1 at 2 m/s. There is a bumper on the second rail car that engages at the moment the cars hit (connecting Car 1 and Car 2), and does not let go. The bumper acts like a spring with spring constant K = 2 N/m. Car 2 is 7 m from the wall at the time of collision (Car 2 is between Car 1 and the wall).
I have attached the work I have done so far, but I'm not understanding how to find x1(t) and x2(t), how we know Car 2 hits the wall (or moves away from it), and at what speed Car 1 travels to stay in place after link-up (given: 1 m/s, but not sure why that is).
Thank you in advance.
Chapter 27 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 27 - A steady-state heat balance for a rod can be...Ch. 27 - 27.2 Use the shooting method to solve Prob. 27.1....Ch. 27 - 27.3 Use the finite-difference approach with to...Ch. 27 - 27.4 Use the shooting method to solve
Ch. 27 - Solve Prob. 27.4 with the finite-difference...Ch. 27 - 27.7 Differential equations like the one solved...Ch. 27 - 27.8 Repeat Example 27.4 but for three masses....Ch. 27 - 27.9 Repeat Example 27.6, but for five interior...Ch. 27 - Use minors to expand the determinant of...Ch. 27 - 27.11 Use the power method to determine the...
Ch. 27 - 27.12 Use the power method to determine the...Ch. 27 - Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.13 to solve...Ch. 27 - 27.15 Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.15 to solve...Ch. 27 - 27.17 Develop a user-friendly program to solve...Ch. 27 - Develop a user-friendly program to solve for the...Ch. 27 - 27.19 Use the Excel Solver to directly solve...Ch. 27 - Use MATLAB to integrate the following pair of ODEs...Ch. 27 - The following differential equation can be used to...Ch. 27 - 27.22 Use MATLAB or Mathcad to...Ch. 27 - 27.23 Use finite differences to solve the...Ch. 27 - Solve the nondimensionalized ODE using finite...Ch. 27 - 27.25 Derive the set of differential equations for...Ch. 27 - 27.26 Consider the mass-spring system in Fig....Ch. 27 - 27.27 The following nonlinear, parasitic ODE was...Ch. 27 - A heated rod with a uniform heat source can be...Ch. 27 - 27.29 Repeat Prob. 27.28, but for the following...Ch. 27 - 27.30 Suppose that the position of a falling...Ch. 27 - Repeat Example 27.3, but insulate the left end of...
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