(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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f9c13e2-5c54-4ec3-b4e3-dc49b76d4e30%2F89635b6f-0f21-47ac-90bb-22107228dc25%2F8efyiks_processed.png&w=3840&q=75)
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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