QUESTION NO 1: The wing is a very flexible part of the airplane. If the frequency of periodic vibration of the gust has a frequency similar to the natural structural frequency of the wing, it will enter resonance aeroelastic flutter and the up and down deflection of the wing will be increased, amplified, and eventually lead to its destruction. Emergence of flutter compromises not only the long term durability of the wing structure, but also the operational safety, flight performance and energy efficiency of the aircraft. Therefore, it is critical to identify the natural frequencies and mode shapes of the wing structure in order to avoid resonance at these frequencies. A passenger airplane wing, can modeled as a three-degree-of-freedom lumped-mass system, as shown in the figure below: I. Please estimate the fundamental frequency of vibration of the system as a function of mass and stiffness, assuming the mode shape and the following system parameters: k= k, k= 2k, k3 = 3k, m1 = m, m = 2m, m3 = 3m II. Please identify which method you are using to estimate the fundamental frequency and why? III. The estimated fundamental frequency is higher or lower than the exact value of fundamental frequency? TOF -1- -13- X1 X2 X3 Figure 1: A) Antonov Aircraft. B) Three degree of Freedom lumped mass system model of Antonov Aircraft Wing