The cylindrical aluminum part shown below is to be modeled using the finite element method. The part is connected to the two walls (indicated with diagonal lines). A load is applied at x = 4 m producing a total force on the structure of F = 2 kN. The length and diameters of the part components are dimensioned on the figure. =2 m ↓ F = 2 kN Ø=1 m 0=2 m Ø=1 m 2 m 4 m 6 m 8 m k1 2 k2 3 k3 k4 5 Model this part using the finite element method in 1 spatial dimension. Use the 4 spring elements shown above. You can ignore the thin component where the load is applied. (a) Compute k₁, k2, k3, and k4. Use the relation k = AE L where A is the cross-sectional area, L is the length, and E is the elastic modulus. For aluminum E = 70 x 109 Pa (or N/m²). (b) Construct the matrices that are used to compute the displacements of each node using the finite element method. Leave the matrices in terms of the variables k₁, k2, k3, and k4. Be sure your matrices satisfy the boundary conditions.