The vibration is 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.a) The model is given in Figure P4. Calculate the natural frequencies and mode shapes. Plot the mode shapes and interpret them according to the airplane's deflection.b) Consider the airplane of Figure P4 with modal damping of with 0.1 in each mode. Suppose that the airplane hits a gust of wind, which applies an impulse of 3?(t) at the end of the left wing and ?(t) at the end of the right wing. Calculate the resulting vibration of the cabin [??2(??)].
c) Consider again the airplane of Figure P4 with 10% modal damping in each mode. Suppose that this is a propeller-driven airplane with an internal combustion engine mounted in the nose. At a cruising speed the engine mounts transmit an applied force to the cabin mass (4m at ??2) which is harmonic of the form 50??????10??. Calculate the effect of this harmonic disturbance at the nose and on the wind tips after subtracting out the translational or rigid motion.