Develop the global stiffness matrix $K$ for uespring assemblage shown below using the fundamental concept of Nodal Force Equilibrium. Show your solution in detail along with neat sketch of the FBD of the spring assemblage.

Also, verify the global stiffness matrix $K$ for the same spring assemblage using the Direct Stiffness Method. Show all steps in detail including the development of the stiffness matrix $k$ for each spring.

In addition, determine the displacements at nodes $2$ and $3$ due to the applied forces; the support reactions; and the force inside each spring. Consider all springs have the same spring constant $)=(400k\frac{N}{m}.$