A single DOF mass-damper-spring system undergoes free damped vibrations, which are relatively fast. A sensing system is utilized to measure the vibration amplitudes, which can capture successive data...

A single DOF mass-damper-spring system undergoes free damped vibrations, which are relatively fast. A sensing system is utilized to measure the vibration amplitudes, which can capture successive data only every five vibration cycles, whereby a constant decay of 50% is noted between two consecutive measurements. Determine the damping ratio that corresponds to this system’s vibrations.