solve each part using MATLAB and Newtons's second law and eagin value to get the frequencies and modes of vibration

A heavy machine tool is mounted on the first floor of a building, as shown in the figure. (a) Derive the equations of motion and solve for the frequencies and modes of vibration for the mentioned stiffnesses and masses. (b) Then simplify these results for the case where all the stiffness parameter values are k = 1 N/m and all the masses parameter values are m= 1 kg. Plot the modes and responses for X:(0) = 0.5 cm and assume that all other initial conditions are equal to zero. (c) For the previous system in (b), suppose that k = (1 + )k = (1 + 0.05)k, where e signifies a stiffness imperfection. Solve for the frequencies and modes of vibration and plot the modes and responses for x7(0) = 0.5 cm and all other initial conditions equal zero. Compare the results with and without imperfections. How do these results compare with those discussed in the section? Discuss. (d) For the previous system in (b), solve assuming m2 = m(1 + ). Use the same parameter values. Discuss. Mass Stiffness (kg) coefficient kN/m) Floor 9000 900 Base and Mounting 2000 900 Machine tool head 400 3500 A heavy machine tool is mounted on the first floor of a building, as shown in the figure. (a) Derive the equations of motion and solve for the frequencies and modes of vibration for the mentioned stiffnesses and masses. (b) Then simplify these results for the case where all the stiffness parameter values are k = 1 N/m and all the masses parameter values are m= 1 kg. Plot the modes and responses for X:(0) = 0.5 cm and assume that all other initial conditions are equal to zero. (c) For the previous system in (b), suppose that k = (1 + )k = (1 + 0.05)k, where e signifies a stiffness imperfection. Solve for the frequencies and modes of vibration and plot the modes and responses for x7(0) = 0.5 cm and all other initial conditions equal zero. Compare the results with and without imperfections. How do these results compare with those discussed in the section? Discuss. (d) For the previous system in (b), solve assuming m2 = m(1 + ). Use the same parameter values. Discuss. Mass Stiffness (kg) coefficient kN/m) Floor 9000 900 Base and Mounting 2000 900 Machine tool head 400 3500