iii$)$ If the spring$-$mass system with mass m $=5$ kg and stiffness k $=100$ kN$/$m described in $($ii$)$ is subjected to a periodic force FoSin$\backslash$omega t $(\backslash$omega is the frequency in rad$/$s$),$ with a forcing frequency of $22$ Hz$,$ explain what will be the response of the system. $(25$ Marks$)$

iv$)$ What would be the response of the spring$-$mass system described in $($ii$),$ if the system has an added damper with the damping coefficient $($a$)$ c value as $30\%$ of the cc$,$ the critical damping of the system, $($b$)$ c value as $100\%$ of the cc$.$ Explain the responses in these $2$ cases. Explain whether the natural frequency of the system will remain same in these $2$ cases.