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(b) Use MATLAB to solve for the displacements .x. Substituting the parameter values 20 -10 0 -10 20-102₂ 0 -10 10 19.62 29.43 24.525 A MATLAB script can be used to obtain the solution for the displacements

(b) Use MATLAB to solve for the displacements .x. Substituting the parameter values 20 -10 0 -10 20-102₂ 0 -10 10 19.62 29.43 24.525 A MATLAB script can be used to obtain the solution for the displacements

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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Solve for the displacements Three masses are suspended vertically by a series of identical springs where mass 1 is at the top and mass 3 is at the bottom. If g = 9.81 m/s², m₁ = 2 kg, m2 = 3 kg, m3 = 2.5 kg, and the spring constant k's = 10 kg/s². (a) For this physical problem, create a system of linear algebraic equations. 0=k(x₂-x₂)+m₁g-kx₁ 0=k(x₂-x₂)+m₂8-k(x₂-x₁) 0=m38-k(x3 -x₂) Terms can be combined to yield 2kx, -kx₂ =m₁g -kx₁ +2kx₂ -kx3 = m₂8 -kx₂+kx3=m3g (b) Use MATLAB to solve for the displacements .x. Substituting the parameter values 20 -10 0 X₁ -10 20 -10 0 -10 10 19.62 29.43 24.525 A MATLAB script can be used to obtain the solution for the displacements clc; format short g g=9.81; k=10; K=[2*k -k 0; -k 2*k -k;0 -k k] (c) Now, for the same masses, calculate the displacements x for k's = 5 kg/s² and 15 kg/s². (d) Plot three graphs showing the relation between the k-values and the displacements, x. (e) What you conclude from the graphs? (f) For all these calcualtions, create one M-file. Inlcude this file with your answers.
Transcribed Image Text:Solve for the displacements Three masses are suspended vertically by a series of identical springs where mass 1 is at the top and mass 3 is at the bottom. If g = 9.81 m/s², m₁ = 2 kg, m2 = 3 kg, m3 = 2.5 kg, and the spring constant k's = 10 kg/s². (a) For this physical problem, create a system of linear algebraic equations. 0=k(x₂-x₂)+m₁g-kx₁ 0=k(x₂-x₂)+m₂8-k(x₂-x₁) 0=m38-k(x3 -x₂) Terms can be combined to yield 2kx, -kx₂ =m₁g -kx₁ +2kx₂ -kx3 = m₂8 -kx₂+kx3=m3g (b) Use MATLAB to solve for the displacements .x. Substituting the parameter values 20 -10 0 X₁ -10 20 -10 0 -10 10 19.62 29.43 24.525 A MATLAB script can be used to obtain the solution for the displacements clc; format short g g=9.81; k=10; K=[2*k -k 0; -k 2*k -k;0 -k k] (c) Now, for the same masses, calculate the displacements x for k's = 5 kg/s² and 15 kg/s². (d) Plot three graphs showing the relation between the k-values and the displacements, x. (e) What you conclude from the graphs? (f) For all these calcualtions, create one M-file. Inlcude this file with your answers.
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