hi all,

I'm trying to grab the idea of the solution sequence of general dynamic anlaysis (modal anlysis) of structures where the general equation of structure stability is

m*x(t)'' + c*x(t)' + k*x(t) = F(t)

where :
"m" is :mass matrix
"c" is :damping coefficent matrix
"k" is :spring coefficent matrix
x(t) is: displacement in sepcified direction

For the modal analys external force ( F(t)=0 ) is equal to 0 to get free-vibaration modes of structure, and if assume that there is no damping case, the equation takes the simple form of

m*x(t)'' + k*x(t)=0;

We have to write this equation for each floor, and later on we assembly the equations where they form the matrixes (mass, damp, etc..).

To solve the problem mathematicians introduce the

|m-w^2|*fi=0

w :eigenvalue ; fi : eigenvector;

But nowhere I have seen that [m*x(t)'' + k*x(t)=0;] can be written as
|m-w^2|*fi=0.

Any help is appreciated!
Best Regards,