$[1]$ For the spring assembly shown below, $[40$pts$]$

i$).$ Draw a system level free body diagram.

ii$).$ Draw a free body diagram for spring $k_3($displacements and forces$).$

iii$).$ Determine the nodal displacements.

iv$).$ Determine reaction forces.

all using Direct Stiffness Method. Given,

$k_1=300\frac{N}{m},k_2=500\frac{N}{m},k_3=800\frac{N}{m},k_4=500\frac{N}{m},k_5=200\frac{N}{m},u_2==2m$