An idealised landing gear system of an aeroplane consists of 3 identical one-degree-of-freedom spring-mass- damper systems as shown in the figure. Construct the equation of motion of the landing gear system. If the runway surface is described as a function of time y(t) =Yocoswt. Assuming that: Y₁ = 0.2m and w = 158rad/s, determine the values of spring stiffness, k, and damping coefficient, c, that limit the amplitude of vibration of the aeroplane to 0.085m when it is landing in the two cases: a. The aeroplane is empty with the total mass of 9500kg. b. The aeroplane is fully loaded with the total mass of 40,000kg x(0)

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.