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3.7 Three balls of equal mass m are joined by identical springs of force constant k (similar to that described in section 3.5). Determine the natural frequencies and normal modes of this system, and sketch the resulting displacements for each mode. Repeat if the middle ball is replaced with one of mass 2m. Using problem 3.7 in the study guide for linear algebra as a reference produce a set of simultaneous equations which describe the behaviour of a system of three balls of mass 1 kg, 2 kg and 4 kg joined by identical springs with spring constants of 5 N/m. Convert to matrix form and determine the Eigen values and Eigen vectors. Use the Eigen values and Eigen vectors to determine the natural frequencies and normal modes of the system.

3.7 Three balls of equal mass m are joined by identical springs of force constant k (similar to that described in section 3.5). Determine the natural frequencies and normal modes of this system, and sketch the resulting displacements for each mode. Repeat if the middle ball is replaced with one of mass 2m. Using problem 3.7 in the study guide for linear algebra as a reference produce a set of simultaneous equations which describe the behaviour of a system of three balls of mass 1 kg, 2 kg and 4 kg joined by identical springs with spring constants of 5 N/m. Convert to matrix form and determine the Eigen values and Eigen vectors. Use the Eigen values and Eigen vectors to determine the natural frequencies and normal modes of the system.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section: Chapter Questions
Problem 7RE
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3.7 Three balls of equal mass m are joined by identical springs of force constant k (similar to that described in section 3.5). Determine the natural frequencies and normal modes of this system, and sketch the resulting displacements for each mode. Repeat if the middle ball is replaced with one of mass 2m.
Transcribed Image Text:3.7 Three balls of equal mass m are joined by identical springs of force constant k (similar to that described in section 3.5). Determine the natural frequencies and normal modes of this system, and sketch the resulting displacements for each mode. Repeat if the middle ball is replaced with one of mass 2m.
Using problem 3.7 in the study guide for linear algebra as a reference produce a set of simultaneous equations which describe the behaviour of a system of three balls of mass 1 kg, 2 kg and 4 kg joined by identical springs with spring constants of 5 N/m. Convert to matrix form and determine the Eigen values and Eigen vectors. Use the Eigen values and Eigen vectors to determine the natural frequencies and normal modes of the system.
Transcribed Image Text:Using problem 3.7 in the study guide for linear algebra as a reference produce a set of simultaneous equations which describe the behaviour of a system of three balls of mass 1 kg, 2 kg and 4 kg joined by identical springs with spring constants of 5 N/m. Convert to matrix form and determine the Eigen values and Eigen vectors. Use the Eigen values and Eigen vectors to determine the natural frequencies and normal modes of the system.
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