The wingtip bending vibration of an aircraft is modeled as a single DOF system with a spring and a mass. The wing is fixed at the root. The natural frequency of the wing is measured to be 6.1 Hz. When a fuel tank weighing 5,400 N is added at the wingtip, the natural frequency reduces to 5.2 Hz. Neglect damping effect. A. Determine the effective mass mi(not including the fuel tank) of the model.
B. Determine the effective stiffness k of the model.
y(t): vertical displacement of the wingtip
n,: effective mass of the wing my: mass of the fuel tank
m2 = m1 + mf
C. Determine the natural frequency (in rad/sec and Hz) when the fuel tank weight is reduced to 3,500 N due to fuel consumption.