Q$3($c$).$ Consider a two$-$degrees$-$of$-$freedom undamped vibratory system has mass matrix and stiffness matrix given by

$[$M$]=[[9,0],[0,1]]$ and $[$K$]=[[27,-3],[-3,3]]$ respectively. The system is subject to the initial conditions given by

x$\_(1)(0)=1$;x$\_(2)(0)=$x$\_(1)^()(0)=$x$\_(2)^()(0)=0.$ Find out the natural frequencies of the system and the corresponding

mode shape vectors. Obtain a general expression for the free vibration response of the system due to the given

initial conditions.