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Question 1: Case Studies: Applications of Linear Algebraic Equations (Mechanical Engineering) SPRING-MASS SYSTEMS Idealized spring-mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed. X₁ 2 xz 5 X₁ ■ I llllllllllll At equilibrium, force-balance equations can be developed defining the interrelationships between the springs. k₂(x₂-x₁) = k₁x₁ k₂ (x₂-x₂)=k₂ (x₂-x k₂(x₂-x₂) = k₂(x₂-x2) F=k_(x₂-x₂) where the K's are spring constants. If k1 through k4 are 100, 50, 80, and 200 N/m, respectively and with a force of 14,700N. www

Question 1: Case Studies: Applications of Linear Algebraic Equations (Mechanical Engineering) SPRING-MASS SYSTEMS Idealized spring-mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed. X₁ 2 xz 5 X₁ ■ I llllllllllll At equilibrium, force-balance equations can be developed defining the interrelationships between the springs. k₂(x₂-x₁) = k₁x₁ k₂ (x₂-x₂)=k₂ (x₂-x k₂(x₂-x₂) = k₂(x₂-x2) F=k_(x₂-x₂) where the K's are spring constants. If k1 through k4 are 100, 50, 80, and 200 N/m, respectively and with a force of 14,700N. www

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1: Case Studies: Applications of Linear Algebraic Equations (Mechanical Engineering) SPRING-MASS SYSTEMS Idealized spring-mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed. 2 H 0 ! llllllllllll 2 Task: Formulate the force-balance equations in matrix Ax=8 form N At equilibrium, force-balance equations can be developed defining the interrelationships between the springs, k₂ (x₂-x₁) = k₁x₁ k₂(x₂-x₂)=k₂ (x₂-x2) k₂(x₂-x₂) = k₂(x₂-x2) F=k_(x₂-x₂) where the K's are spring constants. If k1 through k4 are 100, 50, 80, and 200 N/m, respectively and with a force of 14,700N.
Transcribed Image Text:Question 1: Case Studies: Applications of Linear Algebraic Equations (Mechanical Engineering) SPRING-MASS SYSTEMS Idealized spring-mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed. 2 H 0 ! llllllllllll 2 Task: Formulate the force-balance equations in matrix Ax=8 form N At equilibrium, force-balance equations can be developed defining the interrelationships between the springs, k₂ (x₂-x₁) = k₁x₁ k₂(x₂-x₂)=k₂ (x₂-x2) k₂(x₂-x₂) = k₂(x₂-x2) F=k_(x₂-x₂) where the K's are spring constants. If k1 through k4 are 100, 50, 80, and 200 N/m, respectively and with a force of 14,700N.
Task: Formulate the force-balance equations in matrix Ax-B form A B k₂+k₂ −k₂ 2 -k₂ k₂-k₂-k 3 0 0 0 2 -k₂ k₂+k₂ 3 3 -k₂ k₂+k3 - k3 0 -k₂ k₂+k₁ 3 3 k₁+k₂ −k₂ 1 2 -k₂ 0 2 0 -k₂ 3 0 0 k₁+k₂ −k₂ 2 0 0 -k₂ k₂+k₂ −k₂ 2 2 3 -k₂ 4 -k 0 3 -k 4 k₂+k 3 -K₂ K₂+k₂ - k3 2 2 3 0 k₂+k₁ -k 0 -k₁ 4 0 0 3 0 4 -k k₂+kk 4 -k k 4 4 0 0 4 4 -k 4 X X X X X X X 1 X 3 st 3 x2 1 0 1 H
Transcribed Image Text:Task: Formulate the force-balance equations in matrix Ax-B form A B k₂+k₂ −k₂ 2 -k₂ k₂-k₂-k 3 0 0 0 2 -k₂ k₂+k₂ 3 3 -k₂ k₂+k3 - k3 0 -k₂ k₂+k₁ 3 3 k₁+k₂ −k₂ 1 2 -k₂ 0 2 0 -k₂ 3 0 0 k₁+k₂ −k₂ 2 0 0 -k₂ k₂+k₂ −k₂ 2 2 3 -k₂ 4 -k 0 3 -k 4 k₂+k 3 -K₂ K₂+k₂ - k3 2 2 3 0 k₂+k₁ -k 0 -k₁ 4 0 0 3 0 4 -k k₂+kk 4 -k k 4 4 0 0 4 4 -k 4 X X X X X X X 1 X 3 st 3 x2 1 0 1 H
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Question 2: Case Studies: Applications of Linear Algebraic Equations (Mechanical Engineering) SPRING-MASS SYSTEMS Idealized spring-mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed. X4 W 2 O I H lll lll lll lll At equilibrium, force-balance equations can be developed defining the interrelationships between the springs, k₂(x₂-x₁) = k₁x₁ k₂ (x₂-x₂)=k₂(x₂-x₁) k₂(x₂-x₂) = k₂(x₂-x₂) F=k_(x₂-x₂) where the K's are spring constants. If k1 through k4 are 100, 50, 80, and 200 N/m, respectively and with a force of 14,700N. Refer to your answer in Question 1 Task: Formulate the force-balance equations in matrix Ax-B form applying the given spring constants and force. ***
Transcribed Image Text:Question 2: Case Studies: Applications of Linear Algebraic Equations (Mechanical Engineering) SPRING-MASS SYSTEMS Idealized spring-mass systems have numerous applications throughout engineering. Figure below shows an arrangement of four springs in series being depressed. X4 W 2 O I H lll lll lll lll At equilibrium, force-balance equations can be developed defining the interrelationships between the springs, k₂(x₂-x₁) = k₁x₁ k₂ (x₂-x₂)=k₂(x₂-x₁) k₂(x₂-x₂) = k₂(x₂-x₂) F=k_(x₂-x₂) where the K's are spring constants. If k1 through k4 are 100, 50, 80, and 200 N/m, respectively and with a force of 14,700N. Refer to your answer in Question 1 Task: Formulate the force-balance equations in matrix Ax-B form applying the given spring constants and force. ***
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