For the spring assemblage shown below, derive an analytic expression for the global stiffness matrix using:

For the spring assemblage shown below, derive an analytic expression for
the global stiffness matrix using:
a) the direct stiffness method, and
b) the potential energy method approach.

Code (using MATLAB, or whatever programming language you like) the
mechanical system, where the user will need to provide values for the 5
spring stiffnesses and the program will print-out the global stiffness matrix
and output the unknown displacements in each of the following cases:
a) a horizontal force 2 kN is applied at point 4 (rightwards direction),
b) a horizontal force 2 kN is applied at point 4 (leftwards direction),
c) a horizontal force 1 kN is applied at point 3 (rightwards direction) with
the restriction at point 3 being removed, and
d) a horizontal force 5 kN is applied at point 1 (leftwards direction) with
the restriction at point 1 being removed.
Use the following values: k(1)=10 N/cm, k(2)=20 N/cm, k(3)=30 N/cm,
k(4)=40 N/cm and k(5)=50 N/cm in order to present, analyse and discuss
your numerical results.