Problem $3$: $[15$ pts$]$

Given the translational mechanical system shown, with $k_1=7[\frac{N}{m}],k_2=3[\frac{N}{m}],b=11$

$N*\frac{s}{m}$ and $M=1[kg]$ :

$($a$)$ Write the transfer function $x\frac{s}{F}(s)$

$($b$)$ If the input force $f(t)=2u(t)[N]$ is applied, what is the resulting $x(t)?$