U=kx/2( (q[2]-q[1])^2+(q[3]-q[2])^2)+ky/2(q[6]+q[4]-2 q[5])^2
U2=U /. {q[2]->Sqrt[M/m] q[2],q[5]->Sqrt[M/m] q[5]}
k=Table[Table[ D[U2,q[i],q[j]],{j,1,6}],{i,1,6}]
eigen=Eigensystem[k]
                       kx (m + 2 M)  2 (ky m + 2 ky M)
Out[4]= {{0, 0, 0, kx, ------------, -----------------}, cut
                            m                m

tx=IdentityMatrix[6]
tx[[2,2]]=Sqrt[M/m]
tx[[5,5]]=Sqrt[M/m]

Last[eigen].tx
                                               M        M
Out[8]= {{0, 0, 0, -1, 0, 1}, {0, 0, 0, 2 Sqrt[-], Sqrt[-], 0}, 
                                               m        m
 
                                                  -2 M
>    {1, 1, 1, 0, 0, 0}, {-1, 0, 1, 0, 0, 0}, {1, ----, 1, 0, 0, 0}, 
                                                   m
 
                  -2 M
>    {0, 0, 0, 1, ----, 1}}
                   m

CO2
2438.1 cm^-1
1373.01
641.49
* ? 1+32/12
    3.666666666666667    
* ? (2438/1373)^2
    3.153017114478638    


Ge O2
1061.6
870.1
195.5

 ? 1+32/72.6
    1.440771349862259    
* ? (1061.6/870.1)^2
    1.488618741515112    
