Question

Three masses, m¡ = 2 kg, m2 = 3 kg, and m3 = 1.5 kg, are attached to springs, k1=30 n/m k2= 25 N/m, k3 = 20 N/m, and k4 = 15 N/m, as shown and g = 9.81 m/s².Initially the masses are positioned such that the springs are in their natural length(not stretched or compressed); then the masses are slowly released and move downward to an equilibrium position as shown.= Show that the equilibrium equations of the three masses are(10 points)- \left(k_{1}+k_{2}+k_{3}\right) u_{1}-k_{3} u_{2}=m_{1} g -k_{3} u_{1}+\left(k_{3}+k_{4}\right) u_{2}-k_{4} u_{3}=m_{2} g -k_{4} u_{2}+k_{4} u_{3}=m_{3} g where ul, u2, and u3 are the relative displacement of each mass as shown. 2- Determine the displacement of the three masses using Gaussian Elimination with Scaled Partial Pivoting (show all the steps, use four digits after the decimal point for all results) (20 points). 3- Solve the same system of equations with the Gauss-Jordan elimination method. 4- Estimate the error of the two previous results 5- Compare the two used methods  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11