For the rod $($spring$)$ assemblies shown below, determine the nodal displacements, forces in each

element, and reaction forces. Use direct stiffness method.

Also, verify the stiffness matrix of problem $2)$ using the minimum potential energy approach $($only up to

the point of deriving the global stiffness matrix to compare with the direct stiffness approach result$).$

$k_1=100l\frac{b}{i}n,k_2=300l\frac{b}{i}n,k_3=200l\frac{b}{i}n,F=200lb$