The researchers studied how the location of imbalance affects the dynamic behavior of a high-speed gasoline engine turbocharger with floating ring bearings. They used mathematical equations to analyze the effects of imbalance and non-linear forces on the turbocharger system. By testing different imbalance locations, they found that the vibration and asynchronous components can be controlled by adjusting the imbalance location. This information is valuable for designing dynamic systems and controlling vibrations in high-speed gasoline engine turbochargers.