Solve matrix equation for a particular variable parameter?

Questions
1

Hello, I am struggling with an issue involving vibrations.
This is the problem I want to solve:

Posnetekzaslona_OP_295_CP_.png
Posnetekzaslona_OP_295_CP_.png1366×768 61 KB

Relevant is the cell with function Solve. J represent mass matrix (3 x 3), Kk represents stiffness matrix (3 x 3), M01 is a vector of torque (3 x 1) and fi is vector of rotation (3 x 1) - the vector i am searching for.

What I would like to do is to represent the solution of this equation in animation for changing excitation frequency (w) and I would like to know if someone could help me?

So far I have tried using ListLinePlot for plot of vector fi solutions and use animate on that but it doesnt work as i have to manually evolve fi1, fi2, fi3 from vector to array type.

I am very thankful for all of your help.

2

Here is an attempt:

massMatrix = RandomReal[{0, 1}, {3, 3}];
stiffnessMatrix = RandomReal[{0, 1}, {3, 3}];
m01 = RandomReal[{0, 1}, 3];
sol[\[Omega]_] = 
  Array[fi, 3] /. 
   First@Solve[(-\[Omega]^2*massMatrix + stiffnessMatrix).Array[fi, 
        3] == m01, Array[fi, 3]];
Manipulate[
 Show[ParametricPlot3D[sol[\[Omega]], {\[Omega], 0, 5}], 
  Graphics3D[{Point[{0, 0, 0}], Arrow[{{0, 0, 0}, sol[t]}]}], 
  AxesLabel -> {fi1, fi2, fi3}], {t, 0, 5}]
3

Thanks for help, but this is not excatly what i was looking for. I am trying to plot 2d diagram where i will have points which represent rotation of certain element (vector fi). And i am trying to find especially corealition to excitation frequency omega.

4

I understand you want to solve your equation for fi.

Is it this what you want?

massMatrix = RandomReal[{0, 1}, {3, 3}];
stiffnessMatrix = RandomReal[{0, 1}, {3, 3}];
m01 = RandomReal[{0, 1}, 3];

mm = (-\[Omega]^2*massMatrix + stiffnessMatrix);
mm // MatrixForm

fi = Inverse[mm].m01