IN PYTHON

HW$5\_6$ Three carts, interconnected by springs, are subject to the loads $P_1,P_2$ and $P_3$ as shown in the figure. The

displacements of the carts, $u_1,u_2,$&$u_3$ are governed by the equilibrium equations:

$P_1-k_1{u}_1+k_5(u_3-u_1)+k_4(u_2-u_1)=0$

$P_2-k_2{u}_2-k_4(u_2-u_1)+k_6(u_3-u_2)=0$

$P_3-k_7{u}_3-k_8{u}_3-k_3{u}_3-k_6(u_3-u_2)-k_5(u_3-u_1)=0$

Let $k_1=k_2=k_3=25\frac{N}{m},k_4=k_6=10\frac{N}{m},k_5=5\frac{N}{m},k_7=k_8=2\frac{N}{m}$&$P_1=P_2=P_3=2N.$

Solve for the displacements. Present the results in a complete sentence.