1. A four spring-mass branched system is shown in the figure below. If the masses are moving in the vertical direction only. www KA m m2 www m3 MA X4, X4 X1,X1 X2, X2 a. Write down the potential energy of the system b. Write down the kinetic energy of the system c. Derive the equation of motion using the Lagrange's equation. Represent the equations in matrix form Ma + Kx = 0 where M is the global mass matrix and K is the global stiffness matrix, a is a vector containing the acceleration of masses and x is the displacement vector d. Modify the code from HW1 to also return the mass matrix, taking in masses at each node as input to the function. Write a script to compute the natural frequencies of this system and modes of oscillation for each frequency using Eigen-decomposition. Use k = k2 = 1, k3= k4= 2 N/m, m= m3=m4=1 kg and m2 = 3 kg for part (d).