Question

Consider an airplane wing with a fuel pod mounted at its tip. The pod has a mass of 15 kg when it is empty and 1100 kg when it is full. Calculate the change in the natural frequency of vibration of the wing, as the airplane uses up the fuel in the wing pod.

Answer 1

The change in the natural frequency of vibration of the wing can be calculated using the difference in mass between the empty and full fuel pod. The change in the natural frequency is approximately 20.87 times the initial frequency.

Step-by-step explanation:

The change in the natural frequency of vibration of the wing can be calculated by considering the change in the mass of the fuel pod. The difference in mass between the empty and full fuel pod is 1100 kg - 15 kg = 1085 kg. The natural frequency of vibration of a system is inversely proportional to the square root of its mass, so the change in the natural frequency can be calculated as follows:

Let the initial natural frequency be f0 and the change in mass be ∆m. The change in the natural frequency (∆f) is given by:

∆f/f0 = (∆m/m)1/2

∆f/f0 = (1085 kg/15 kg)1/2 ≈ 20.87

Therefore, the change in the natural frequency of vibration of the wing is approximately 20.87 times the initial frequency.