Consider the spring assembly shown below. A geometry is discretized into a spring assembly of four elements and five nodes. The spring assembly is fixed between the edges of a wall as shown. A force P is applied laterally at the third node, which causes the springs to deform along their primary axes. Each spring has a uniform stiffness coefficient of k$.$ Please answer the following questions. You may use a calculator to invert matrices if necessary.

a$)$ bDetermine the global stiffness matrix K

b$)$ Determine the global force matrix F

c$)$ Set up the problem as F $=$ Kd before applying boundary conditions

d$)$ Identify and apply boundary conditions to the problem

e$)$ Determine the displacement of the second, third and fourth nodes

f$)$ Determine the reaction forces at the first and fifth nodes