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How to add unknow parameter in matrix and solve it by use det() syntax for finding w

37 vues (au cours des 30 derniers jours)
% under is what i did but seen it is not work for det(A) for find w
clc % clear history command and past result
syms w;
m1 = 1.8;
m2 = 6.3;
m3 = 5.4;
m4 = 22.5;
m5 = 54;
c2 = 10000;
c3 = 500;
c4 = 1500;
c5 = 1100;
k2 = 1*10^8;
k3 = 50*10^3;
k4 = 75*10^3;
k5 = 10*10^3;
% Form of matrix is Ax=b
% Where A is nxn matrix, x is displacement of lumped masses and b is RHS.
A= [0, 0, 0, 0, (m5*w^2)-k5-c5;
0, 0, k4+c4, -k4-c4+(m4*w^2)+k5+c5, -k5+c5;
k2+c2, -k3-c3-k2-c2+(m2*w^2), k3+c3, 0, 0;
-k2-c2+(m1*w^2), k2+c2, 0, 0, 0];
det (A);
  2 commentaires
Torsten
Torsten le 9 Mai 2024
Your matrix is 4x5. How do you want to define a determinant for it ?
Trong Nhan Tran
Trong Nhan Tran le 9 Mai 2024
sry i missed one comma when typing

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Réponse acceptée

Hassaan
Hassaan le 9 Mai 2024
Modifié(e) : Hassaan le 9 Mai 2024
clc; % Clear command window
clear; % Clear workspace
syms w; % Define w as a symbolic variable
% Define masses, damping coefficients, and stiffness coefficients
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54;
c2 = 10000; c3 = 500; c4 = 1500; c5 = 1100;
k2 = 1*10^8; k3 = 50*10^3; k4 = 75*10^3; k5 = 10*10^3;
% Define the matrix A
A = [k2+c2, -k2-c2+(m2*w^2), 0, 0, 0;
-k2-c2, k2+c2+k3+c3, -k3-c3, 0, 0;
0, -k3-c3, k3+c3+k4+c4, -k4-c4+(m4*w^2), 0;
0, 0, -k4-c4, k4+c4+k5+c5, -k5-c5;
0, 0, 0, -k5, k5+c5+(m5*w^2)];
% Calculate the determinant of the matrix A
detA = det(A);
% Display the determinant
disp('The determinant of matrix A is:');
The determinant of matrix A is:
disp(detA);
double(solve(detA==0,w,'MaxDegree',3))
ans =
1.0e+02 * 0.0000 + 0.0369i 0.0000 + 1.0353i 0.0000 - 0.2352i -0.0000 - 0.0369i -0.0000 - 1.0353i -0.0000 + 0.2352i
-----------------------------------------------------------------------------------------------------------------------------------------------------
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  5 commentaires
Sam Chak
Sam Chak le 10 Mai 2024
Could you explain what the symbolic variable w is?
syms w W
% Define masses, damping coefficients, and stiffness coefficients
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54;
c2 = 10000; c3 = 500; c4 = 1500; c5 = 1100;
k2 = 1*10^8; k3 = 50*10^3; k4 = 75*10^3; k5 = 10*10^3;
% Define the matrix A
A = [k2+c2, -k2-c2+(m2*w^2), 0, 0, 0;
-k2-c2, k2+c2+k3+c3, -k3-c3, 0, 0;
0, -k3-c3, k3+c3+k4+c4, -k4-c4+(m4*w^2), 0;
0, 0, -k4-c4, k4+c4+k5+c5, -k5-c5;
0, 0, 0, -k5, k5+c5+(m5*w^2)];
% Calculate the determinant of the matrix A
detA = det(A);
detA = subs(detA, w^2, W);
% Display the determinant
disp('The determinant of matrix A is:');
The determinant of matrix A is:
disp(detA);
Wsol = double(solve(detA==0, W, 'MaxDegree', 3))
Wsol =
1.0e+04 * -0.0014 + 0.0000i -1.0718 + 0.0000i -0.0553 - 0.0000i
Torsten
Torsten le 10 Mai 2024
I dont know why but when i use det(A) the error is Matrix must be square.
Maybe you used the 4x5 matrix you posted first.

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Plus de réponses (2)

John D'Errico
John D'Errico le 9 Mai 2024
Modifié(e) : John D'Errico le 9 Mai 2024
syms w;
m1 = 1.8;
m2 = 6.3;
m3 = 5.4;
m4 = 22.5;
m5 = 54;
c2 = 10000;
c3 = 500;
c4 = 1500;
c5 = 1100;
k2 = 1*10^8;
k3 = 50*10^3;
k4 = 75*10^3;
k5 = 10*10^3;
% Form of matrix is Ax=b
% Where A is nxn matrix, x is displacement of lumped masses and b is RHS.
A = [k2+c2, -k2-c2+(m2*w^2), 0, 0, 0;
-k2-c2, k2+c2+k3+c3, -k3-c3, 0, 0;
0, -k3-c3, k3+c3+k4+c4, -k4-c4+(m4*w^2), 0;
0, 0, -k4-c4, k4+c4+k5+c5, -k5-c5;
0, 0, 0, -k5, k5+c5+(m5*w^2)];
A
A = 
Assuming that is correctly your matrix, the result will be a degree 6 polynomial.
Adet = det(A)
Adet = 
There can be no exact algebraic solutions fro a degree 5 or higher polynomial. But you can have numerically computed roots.
wsol = solve(Adet,maxdegree = 6)
wsol = 
As you can see, there were no real solutions. All solutions were purely imaginary. The real parts of those solutions are all effectively zero.

john
john le 22 Mai 2024 à 13:37
Modifié(e) : john le 23 Mai 2024 à 11:07
To add an unknown parameter in a matrix and solve it using det() syntax for an IQ brain test, replace an element with 'w.' Then, compute the determinant and solve the resulting equation for 'w.' This process allows for a more dynamic and challenging matrix calculation, enhancing the complexity of the IQ brain test.

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