An optical table with its content weighing $147$ N is to be protected against nearby

vibrations by attaching a weight of $29\mathrm{.}4$ N with the table. The weight is attached using an

elastic cable of stiffness $50$ N$/$m$.$ The table is supported on four columns each of stiffness

$50$ N$/$m$.$ Assuming vibrations take place in only vertical plane $($a$)$ draw the $2$DOF model of

the situation given $($b$)$ write down the EOM $($c$)$ solve for the frequencies $($d$)$ modes of

vibration and $($e$)$ the response of the two masses if x$1($t $=0)=1$ cm and all other initial

conditions are zero.