Please solve only using MATLAB

Figure is a schematic of the four story shear building. Each floor is represented by its mass and the superstructure supporting each floor is idealized by a spring constant representing resistance to lateral motion and a damping coefficient providing frictional energy losses. External forces applied to each floor are ignored in this model, but the base (or the ground) may move during an earthquake. Hence, only four degrees of freedom are needed to describe total displacements of the structure, described as Figure 2. Task a: If the analysis is limited to horizontal motion of the structure, derive the general ODEs for this system. Assume there are no external forces applied to each mass. Your equations should include displacement of the base y() (You may need to look at section 9.5 in week 9 or the 2016 assignment for mechanical students) and damping factors. Then re-write your second order ODEs into a group of first-order ODEs. Task b: Develop a general code named four_dof. which includes the base motion and damping. Use the function Follow the example of two-dof. Use the code developed in Task b to simulate the dynamics of this structure from The initial conditions are v_1 = 0.012m/s, v_2 = 0.032 m/s, v_3 = 0.055 m/s, v_4 = 0.071 m/s, x_1 = 0, x_2 = 0, x_3 = 0, x_4 = 0. Other parameters are M_1 = 3900kg M_2 = 3600kg, M_3 = 3500kg, M_4 = 2500kg, k_1 = 3400 k_2 = 2800 k_3 = 23000 and k_4 = 1800 Igore the base motion and dumping in this calculation. Present your results as time-series plots of displacement of each floor in the same plot. Task c: Write your differential equations in a matrix form. Develop a code named four_dot_matrix. to find the natural frequencies of the building i the damping between different floors are ignored. Use the same data for the masses and stiffness in Task b. Follow the example of two_dof_matrix.m Print the corresponding eigenvectors and natural circular frequencies of vibrations. Show the four modal shapes of vibration and associated natural frequencies of vibration