Do a program in fortran that could solve the next problems where you need to show the code,steps of solutions and results

$1.-$ There is a system of three masses, m$1,$ m$2,$ m$3$ and four springs with elastic constants k$1,$ k$2,$ k$3,$ k$4,$ as shown in the following figure. Write the differential equations of motion and, using a suitable solution proposal, convert the system of three coupled differential equations into a matrix problem of eigenvalues. If m$1=1$kg$,$ m$2=2$ kg $,$ m$3=3$kg$,$ k$1=1$ N$/$m$,$ k$2=2$ N$/$m$,$ k$3=3$ N$/$m$,$ k$4=4$ N$/$m$,$ find the normal modes of vibration of the system, finding the characteristic polynomial using Newton's interpolation method. Likewise, in this same diagram, determine the corresponding normalized eigenvectors.

$2.-$ From the matrix obtained in the previous problem, using the power method in its different variants, find the eigenvalues $$of said matrix, as well as its eigenvectors and its normal vibration modes.