Consider the spring assembly shown in Fig.$\mathrm{}$

$($a$)$ Obtain the global stiffness matrix for the full spring assembly. Take the determinant

of the matrix you obtained $($you can do this using software, e$.$g$.$ Matlab or NumPy$)$

and report what you get. Does your result confirm that the global stiffness matrix is

singular? $($Recall$,$ if the determinant of a matrix is zero, the matrix is singular.$)$

$($b$)$ Write the full matrix equations, substituting in the displacement boundary conditions

and prescribed load.

$($c$)$ Write the reduced matrix equations in terms of only the unknown nodal displacements.

Take the determinant of the reduced system matrix and verify that the reduced stiffness

matrix is not singular. Solve for the nodal displacements.

$($d$)$ Solve for the reaction forces.

1 k = 400 kN/m 2 ww k = 700 kN/m ww 2 k = 400 kN/m 3 ww 3 kN k2 = 400 kN/m www M 4 k = 700 kN/m www 5