$(25$ pts$)$ Consider the spring assemblage

a$.(15$ pts$)$ Determine the displacements of the nodes. Use direct stiffness method to

assemble the global SLE. Apply boundary conditions via the penalty approach.

Important: make sure that the element numbers, local degrees of freedom $($nodal

displacement numbers$),$ global coordinate axis, and global degrees of freedom are shown

in your picture.

b$.(5$ pts$)$ Reassemble the global SLE using the minimum potential energy approach.

c$.(5pts)$ Find reaction forces at the points where spring elements are attached to walls.

d$.(5$ pts$)$ Use the shape functions to find the displacement of the point originally located

$4($in$)$ to the right from the left end of the $800l\frac{b}{i}n$ spring. Assume that the undeformed

length of the $300l\frac{b}{i}n$ spring is $7($in$),$ and the undeformed lengths of the $800l\frac{b}{i}n$ and

$500l\frac{b}{i}n$ springs are $8($in$)$ each.