Solving Determinant w/ Symbolic Values?

I essentially have this determinant here that I need to solve:

Just not sure how to do it symbolically in MATLAB without values...

Also, is there a way that I could then solve for w(omega) smybolically?

Answer 1

[Star Strider]

If you have the Symbolic Math Toolbox, use the symbolic det function:

syms m1 m2 k1 k2 w
M = [(-m1*w^2 + k1)  (-k1);  (-k1)  (-m2*w^2 + k1 + k2)];
detM = det(M);
w = solve(detM,w)

[미선 전]

Thank you!

[미선 전]

you are my god

[Star Strider]

My pleasure!

Thank you!

(A Vote would be appreciated!)

[Aditya Vikram Singh]

@Star Strider can you please also tell how to obtain the fourth degree equation in omega here with coeffiecient of each term in omega.

Answer 2

[Carlen]

Awesome thanks! If I wanted to solve for w^2 instead of w is there a way to do that?

[Star Strider]

My pleasure!

Probably the easiest way to solve for w^2 is simply to substitute w2 for it:

syms m1 m2 k1 k2 w w2
M = [(-m1*w2 + k1)  (-k1);  (-k1)  (-m2*w2 + k1 + k2)];
detM = det(M);
w2 = solve(detM, w2)

That produces two quadratic roots.

If you want to use the roots as a function in other MATLAB code, use matlabFunction and its friends. It is much easier than coding it yourself, and it also vectorises the expression in the process.

For example:

wsq = matlabFunction(w2);
detmat = wsq(3, 5, 7, 13);

will produce a (2x1) vector of solutions.

Answer 3

[Carlen]

Thanks a lot for the help!

[Star Strider]

My pleasure!

Answer 4

[Caio Contezini]

Star Strider, how can I solve that if I dont have Symbolic Math Toolbox?