$(20\%)($i$)$ Determine the material, geometrical and equilibrium equations of the two$-$spring system shown

in the figure below. $($Note: the elongation of spring $1$ and $2$ are denoted with ${}_1,{}_2$ respectively$).(15\%)$

$($ii$)$ Determine the load$-$displacement relationship of the system. $(5\%)$

$($Hint: final equations can be written in matrix form.$)$ DONTTTTT USEEEEEE AI$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$