The block diagram representing a mechanical system is shown in Figure $1.$ The desired set point to controllers is F$($s$)=1/$s$.$ The system vibrates as shown in Figure $2.$

$($i$)$ Find the transfer function of X$($s$)/$F$($s$)$ by reducing the block diagram

$($ii$)$ Determine the value of a and b

$($iii$)$ Find the steady state error of the system