When testing the landing-gear unit of a space vehicle, drop tests are carried out. Figure 11.17 is a schematic model of the unit at the instant when it first touches the ground. At this instant the spring is fully extended and the velocity of the mass is √(2gh), where h is the height from which the unit has been dropped. Obtain the equation representing the displacement of the mass at time t > 0 when M = 50 kg, B = 180Nsm^–1 and K = 474.5Nm^–1, and investigate the effects of different dropping heights h. (g is the acceleration due to gravity, and may be taken as 9.8ms^–2.)

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elele M B x(t) Figure 11.17 Landing gear