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Connected automated vehicles (CAVs), built upon advanced vehicle control and communication technology, can improve traffic throughput, safety, and energy efficiency. Previous studies on CAVs control focus on instability and stability properties of CAV platoons; however, these analyses cannot reveal the damping platoon oscillation characteristics, which are important for enhancing CAV platoon reliability against variant continuous perturbations. To this end, this research seeks to characterize the damping oscillations of CAVs through exploiting the platoon's unforced oscillatory, i.e., damping behavior. Inspired by the mechanical vibration theory, the proposed approach is applied to a CAV platoon with linear car-following control formulated as Helly's model and the predecessor-following communication topology. The proposed approach is applied to a CAV platoon with the linear car-following control formulated as Helly's model and the predecessor-following communication topology. Numerical analysis results show that a periodic perturbation with the resonance frequency of the CAV platoon will amplify the oscillation and lead to the severest oscillatory traffic. Our analysis highlights the importance of preventing platoon oscillations from resonance in ensuring CAV platooning reliability.