For the spring assemblage shown in figure, obtain

$($a$)$ the global stiffness matrix by the direct stiffness method.

Let $k^{(1)}=1ki\frac{p}{i}n,k^{(2)}=2ki\frac{p}{i}n,k^{(3)}=3ki\frac{p}{i}n,k^{(4)}=4ki\frac{p}{i}n,k^{(5)}=5ki\frac{p}{i}n.$

$($b$)$ apply a concentrated force of $2$ kips at node $2$ in the positive $x$ direction and determine the

displacements at nodes $2$ and $4.$