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Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x and y be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m1 = 2 kg and m2 = 1 kg, and the spring constants are ki = 64 N/m and k2 = 32 N/m. a. Set up a system of second-order differential equations that models this situation. This situation is the same model as discussed in class except that there is no third spring, i.e., kz = 0. b. Compute the eigenvalues of the coefficient matrix A and find a corresponding eigenvector for each one. You must get all six entries correct to receive credit.

Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x and y be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m1 = 2 kg and m2 = 1 kg, and the spring constants are ki = 64 N/m and k2 = 32 N/m. a. Set up a system of second-order differential equations that models this situation. This situation is the same model as discussed in class except that there is no third spring, i.e., kz = 0. b. Compute the eigenvalues of the coefficient matrix A and find a corresponding eigenvector for each one. You must get all six entries correct to receive credit.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 25EQ
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Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x and y be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m1 = 2 kg and m2 = 1 kg, and the spring constants are k1 = 64 N/m and k2 = 32 Ñ/m. a. Set up a system of second-order differential equations that models this situation. This situation is the same model as discussed in class except that there is no third spring, i.e., k3 = 0. x" b. Compute the eigenvalues of the coefficient matrix A and find a corresponding eigenvector for each one. You must get all six entries correct to receive credit. The eigenvalue O has an eigenvector The eigenvalue has an eigenvector c. Calculate the natural frequencies w of the system and enter them as a comma separated list. d. Find the general solution to this system of differential equations. Use a1, a2, b1 , b2 to denote arbitrary constants, and enter them as a1, a2, b1, b2. x(t) = y(t) =
Transcribed Image Text:Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two springs, one of which is attached to the wall, as shown in the figure. Let x and y be the displacement of the first and second masses from their equilibrium positions. Suppose the masses are m1 = 2 kg and m2 = 1 kg, and the spring constants are k1 = 64 N/m and k2 = 32 Ñ/m. a. Set up a system of second-order differential equations that models this situation. This situation is the same model as discussed in class except that there is no third spring, i.e., k3 = 0. x" b. Compute the eigenvalues of the coefficient matrix A and find a corresponding eigenvector for each one. You must get all six entries correct to receive credit. The eigenvalue O has an eigenvector The eigenvalue has an eigenvector c. Calculate the natural frequencies w of the system and enter them as a comma separated list. d. Find the general solution to this system of differential equations. Use a1, a2, b1 , b2 to denote arbitrary constants, and enter them as a1, a2, b1, b2. x(t) = y(t) =
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