Calculate the unknowns values that satisfy determinant of matrix equals to zero

Hello everyone,

I'll try to be syntetic :

- I have a system : Mx'' +Cx' +Kx = 0 (M, C and K are matrices of size [m x n] and x a vector [mx1] - I say that x=A exp(i*w*t) (with w the pulsation and t the time) - I have (-w²M + C iw + K)A = 0

I want to find the values w (w is an unknown vector [m x 1]) that satisfy determinant (-w²M + C iw + K)=0 and I don't know if it is possible or not, and if it's possible how can I do ?

Thank you.

[Star Strider]

It seems that ‘w’ could be an eigenvalue. Explore the eig function (and its friends) to see if it will do what you want.

Answer 1

[Soumya Saxena]

I understand that you would like to determine the values of "w" that satisfy the equation, (-w²M + C iw + K)=0. However, in order to better understand your question and provide you with a suggestion, please provide me some more information :

1. What is your use case ? What physical system are you modelling ?

2. What is the end goal that you are trying to achieve ?

3. As mentioned in the post, (-w²M + C iw + K) is the determinant of a matrix. Could you please let me know what matrix it is and how you are defining it ?

4. Please also provide me the exact values of M, C and K, and how you are initializing them.

In general, the unknowns values that make the determinant 0 are the roots of the characteristic equation and are the eigenvalues. To calculate eigenvalues, you may use the "eig" function as given in the following documentation:

https://www.mathworks.com/help/matlab/ref/eig.html