A vibrometer is used to measure the vibration of an engine whose operating-speed range is from \(500 \mathrm{rpm}\) to \(2000 \mathrm{rpm}\). The vibration consists of two harmonics. The amplitude distortion must be less than 3\%. Find the natural frequency of the vibrometer if (a) the damping is negligible and (b) the damping ratio is 0.6 .