A spring assemblage with arbitrarily numbered nodes is shown in the following figure. A force of $6000$ lb is applied at node $4$ and the spring constants are given in the figure. Nodes $1$ and $2$ are fixed. Take the right side of the x axis as positive direction and apply the finite element method to obtain:

a$).$ the global stiffness matrix

b$).$ the displacements of nodes $3$ and $4($Hint: recall Hooke's Law$)$

c$).$ the reaction forces at nodes $1$ and $2,$ and

d$).$ the forces in each spring.