Consider a spacecraft undergoing vibration test on the ground. For vertical vibration, the spacecraft is modeled as a SDOF system. The landing gear consists of gas balloons. The natural frequency of the free vibration is measured at a given pressure. Subsequently, the gas pressure is reduced, and the natural frequency is measured. It turns out that the new frequency is reduced to 80% of the original frequency A. Estimate the reduction in the stiffness of the system by determining a nondimensional quantity R defined as follows:
R= kold -knew/ kold
B. Estimate the increase (in percent) in the static displacement.