When testing the landing-gear unit of a space vehicle, drop tests are carried out. Figure 5.17 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 = 180 N s m-1 and
K = 474.5 N m-1, and investigate the effects of different dropping heights h. (g is the acceleration due to gravity, and may be taken as 9.8 m s-2.)