QUESTION $1(40\%)$

For the following system shown in Figure $1,$ all the points move parallel to the collinear springs. One node of the system is fixed, and the other node is moved $1$ meter towards the left. $P=100N$ and $k=10\frac{N}{m}.$ Answer the following questions:

a$)$ Find the global stiffness matrix and force vector? $(10\%)$

b$)$ Find the displacements of each node using MATLAB? $(10\%)$

c$)$ Find the internal loads of each spring using MATLAB? $(10\%)$

d$)$ Verify the results from part b and part c using ANSYS? $(10\%)$

Figure $1$: The representation of the model