A motor-generator set is designed with steady-state operating speed between 2000 and 4000 rpm. Unfortunately, due to an imbalance in the machine, a large violent vibration occurs at around 3000 rpm.
An initial absorber design is implemented with a mass of 2 kg tuned to 3000 rpm. This, however, causes the combined system natural frequencies to occur at 2500 and 3500 rpm.
Redesign the absorber so that ω1 6 2000 rpm and ω2 7 4000 rpm, rendering the system safe for operation.