Question for using root function.

% Using the MATLAB function “roots”  for find non-zero natural frequencies

% define symbolic variable w
syms w;
% Given parameters
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54; 
c2 = 10; c3 = 0.5; c4 = 1.50; c5 = 1.1;
k2 = 100000; k3 = 50; k4 = 75; k5 = 10;
% Set up system matrices
% mass matrix
M = diag([m1, m2, m3, m4, m5]); 
% damping matrix 
C = [c2 -c2 0 0 0;
    -c2 c2+c3 -c3 0 0;
    0 -c3 c3+c4 -c4 0;
    0 0 -c4 c4+c5 -c5;
    0 0 0 -c5 c5]; 
% stiffness matrix
K = [k2 -k2 0 0 0;
    -k2 k2+k3 -k3 0 0;
    0 -k3 k3+k4 -k4 0;
    0 0 -k4 k4+k5 -k5;
    0 0 0 -k5 k5]; 
% Calculate frequency equation
Zw = w^2*M + 1i*w*C + K; % impedance matrix
freqEq = det(Zw); % take determinant to get frequency equation
pretty(simplify(freqEq)); % display simplified frequency equation

% Display the non-zero natural frequencies
disp('Non-zero natural frequencies (Hz):');
disp(root(freqEq))

[John D'Errico]

Please stop posting the same question multiple times. If you want to expand on a question, then do so by editing the question, or by adding a comment. I closed the last question as a duplicate. In fact, since this is now at least the third time you asked this question...

[Trong Nhan Tran]

Sry i closed the last one. I had figured out how to do it, so this is my new question to use root to find natural frequency

[Torsten]

disp(vpa(root(freqEq)))

instead of

disp(root(freqEq))

[Trong Nhan Tran]

Error using indexing (line 918)

Invalid MATLAB indexing or symbolic function definition. Symbolic function arguments must be symbolic variables

and function body must be convertible to sym expression.

Error in PartA_b (line 37)

disp(vpa(root(freqEq)))

Related documentation

I got this error when i used disp(root(freqEq))

[Torsten]

If you use the code from above, you won't get this error (at least if you work with MATLAB R2024a).

syms w
% Given parameters
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54; 
c2 = 10; c3 = 0.5; c4 = 1.50; c5 = 1.1;
k2 = 100000; k3 = 50; k4 = 75; k5 = 10;
% Set up system matrices
% mass matrix
M = diag([m1, m2, m3, m4, m5]); 
% damping matrix 
C = [c2 -c2 0 0 0;
    -c2 c2+c3 -c3 0 0;
    0 -c3 c3+c4 -c4 0;
    0 0 -c4 c4+c5 -c5;
    0 0 0 -c5 c5]; 
% stiffness matrix
K = [k2 -k2 0 0 0;
    -k2 k2+k3 -k3 0 0;
    0 -k3 k3+k4 -k4 0;
    0 0 -k4 k4+k5 -k5;
    0 0 0 -k5 k5]; 
% Calculate frequency equation
Zw = w^2*M + 1i*w*C + K; % impedance matrix
freqEq = det(Zw); % take determinant to get frequency equation
pretty(simplify(freqEq)); % display simplified frequency equation

         10    9                               8    7                                6
3720087 w     w  2875076127i   13291777051299 w    w  1518467207049i   353165987709 w     5                              4    3                              2
----------- + -------------- + ----------------- + ----------------- + --------------- + w  34610882040i + 829211728500 w  + w  47283750000i + 337500000000 w
     50            5000               2500                500                 2

% Display the non-zero natural frequencies
disp('Non-zero natural frequencies (Hz):');

Non-zero natural frequencies (Hz):

%disp(root(freqEq))
disp(vpa(root(freqEq)))

[Trong Nhan Tran]

I dont know what is the wrong here about my code or somthing cuz looking like the answer is 100% worng, the number is too small and a lot of frquencies instead of 5 degree of freedoms. I no idea what wrong with this.

[Torsten]

I don't have experience with the physical background of your equations.

Just solving your system for omega gives a similar result as yours - only the 1i's are missing.

syms w
% Given parameters
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54; 
c2 = 10; c3 = 0.5; c4 = 1.50; c5 = 1.1;
k2 = 100000; k3 = 50; k4 = 75; k5 = 10;
M1 = [-k2, k2, 0, 0, 0;k2, -k3-c3-k2, k3+c3, 0, 0;0, k3, -k4-c4-k3, k4+c4, 0;0, 0, k4, -k5-c5-k4, k5+c5;0, 0, 0, k5, -k5];
M2 = [-c2, c2, 0, 0, 0;c2, -c2, 0, 0, 0;0, c3, -c3, 0, 0;0, 0, c4, -c4, 0;0, 0, 0, c5, -c5];
M3 = diag([m1,m2,m3,m4,m5]);
M = M1+w*M2+w^2*M3;

ans = 

vpa(root(det(M)==0))

ans = 

[Trong Nhan Tran]

is it m1 is for matrix of stifness and m2 is damping?

[Torsten]

I just wrote your system of equations in matrix form

M(w)*[X1;X2;X3;X4;X5] = 0

and determined the values of w for which the equation has a nontrivial solution.

[Trong Nhan Tran]

but i think M1 was wrong cuz it has c in stiffness matrix

K = [k2 -k2 0 0 0;

-k2 k2+k3 -k3 0 0;

0 -k3 k3+k4 -k4 0;

0 0 -k4 k4+k5 -k5;

0 0 0 -k5 k5];

[Torsten]

Write your equations (1)-(5) as

M1*[X1;X2;X3;X4;X5] + w*M2*[X1;X2;X3;X4;X5] + w^2*M3*[X1;X2;X3;X4;X5] = 0

and you will see that my M1, M2 and M3 matrices are correct to reproduce your system.

But as I said: I don't know if this is how "natural frequencies" are defined.