$6.$ Do $5\mathrm{.}62$ in Thomson$/$Dahleh text

$7.$ Continue with the system of problem $5\mathrm{.}62$ for the case of m$1=1$ kg$,$ m$2=1$ kg$,$ and m$3=2$ kg$,$ k$1=$ k$2=$ k$4=$ k$5=2$ N$/$m$,$ and k$3=25,$ and find the mode shapes and normalize them with respect to the mass matrix.

$8.$ Continuing with the previous problem, use orthogonality to write the free vibration response to the initial conditions x$1(0)=$ x$2(0)=$ x$3(0)=2$ m$,$ and m$/$s$.$