Question: Why Det(C) doen't works ?

Hello everybody,

#I have 2 odes

ode[1]:=42.62500000*(diff(Theta[1](t), t, t))+12.00000000*(diff(Theta[2](t), t, t))+1400*Theta[1](t)-1000*Theta[2](t) = 0;
ode[2]:=12.00000000*(diff(Theta[1](t), t, t))+5.475000000*(diff(Theta[2](t), t, t))+1000*Theta[2](t)-1000*Theta[1](t) = 0;

#I know  the solution Theta[i]= A[i] cos ( omega*t) it gives Theta[i]= A[i] and diff (Theta[i],t)=omega^2*A[i]
#So, I have transformed my Odes like this:

ode[1]:=(12.00000000*omega^2-1000.)*A2+(42.62500000*omega^2+1400.)*A1 = 0;
ode[2]:=(5.475000000*omega^2+1000.)*A2+(12.00000000*omega^2-1000.)*A1 = 0;

#then I put this coefficients in a matrix
C := Matrix(2, 2, {(1, 1) = 42.625*omega^2+1400, (1, 2) = 12.*omega^2-1000., (2, 1) = 12.*omega^2-1000, (2, 2) = 5.475*omega^2+1000.});

#then I look for the determinant =0

Det(C);


Why Maple don't calculate Det(C)? after I will do solve ( Det(C)=0,{A[1],A[2]});

Is there a faster way to find the eigenvalues of odes? ( because eigenvalues and eigenvector are used only with matrix)

Thanks a lot
Ternox