## second order differential in modal anlays

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,