The vibration in the vertical direction of an airplane and its wings can be modeled as a three-degree-of-

freedom system with one mass corresponding to the right wing, one mass for the left wing, and one

mass for the fuselage. The stiffness connecting the three masses corresponds to that of the wing and is a

function of the modulus E of the wing. The equation of motion is: Mi+Kx=0 M and K are the mass and stiffness matrices respectively. The model is illustrated below. . [(1, ‘1‘" I J " Solve for the free response of the system both analytically (by hand calculations) and computationally

(using MatLab), where E = 6.9 x 109 N/m,l = 2 m, m = 3000 kg, and I = 5.2 x 10‘6 m4. Let the initial

displacement correspond to a gust of wind that causes an initial condition of x(0) = [0.2 0 0]T m and

5r(0) = 0. Plot the displacement of each mass versus time for 10 seconds.