As presented in Figure 1, a control tab of an airplane elevator is hinged about an axis in the elevator, shown as the point O, and activated by a control linkage behaving like a torsional spring of stiffness k,. The mass moment of inertia of the control tab is 1,, so that the natural frequency of the system is w, = k, / 1, - Because k, cannot be calculated exactly, it is necessary to obtain the natural frequency w, experimentally. To this end, the elevator is held fixed and the tab is excited harmonically v)=A cos(ot) with A is a constant) by means of the spring k, while restrained by the spring k,, and the excitation frequency w is varied until the resonance frequency a, is reached. Question: Caleulate the natural frequency w, of the control tab in terms of w, and the parameters of the experimental setup. Free Body Diagram Control t-b