Write MATLAB or PYTHON software that will calculate $(1)$ the equilibrium displacements, $(2)$ the internal stresses and $(3)$ the elongations of a spring$/$mass system using the $3$ steps discussed in class and in the book. Solve the force balance first, then back$-$calculate the elongation and internal stress vectors using the displacements. Your code should be created in a general way where the user will input the following: the number of springs$/$masses$,$ the spring constants for each spring, the masses, and which boundary condition to apply. Your code should allow the user to apply one or two fixed ends.

For this project, you will need to solve $Ku=f.$ You will calculate the condition number of K by $(1)$ calculating and printing the singular values $($and eigenvalues$)$ using YOUR SVD algorithm, and $(2)$ calculating and printing a $I_2-$condition number. Do not use a software call to calculate a condition number. USE YOUR SVD ROUTINE TO SOLVE THE KU$=$F SYSTEM!

Lastly, examine and discuss what happens when two free ends are used as boundary conditions.

Point distribution:

$20$ pts $-$ one fixed end, one free end successful algorithm

$20$ pts $-$ two fixed ends successful algorithm

$10$ pts $-$ two free end examination

$10$ pts $-$ calculating matrix condition number for $K$ for each user supplied system