Question $2$

a$)$ For the spring$-$mass system shown in Figure $2$a$,$ given that $K=6\frac{N}{m},f_v=5N\frac{s}{m^2},$ and $M=1kg,$ where $K,f_v$ and $M$ are spring constant, coefficient of viscous friction, and mass respectively. Determine the transfer function, $G(s)=x\frac{s}{F}(s)$

$[15$ Marks$]$

b$)$ Determine the state space equation of a single mass moving in a one$-$dimensional direction $($x$)$ under force $($F$).($See Fi$.$men $2h)$

$[15$ Marks$]$