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Nonlinear aeroelastic limit-cycle oscillations (LCOs) have become an area of interest due to both detrimental effects on flying vehicles and use in renewable energy harvesting. Initial studies on the interaction between aeroelastic systems and incoming flow disturbances have shown that disturbances can have significant effects on LCO amplitude, with some cases resulting in spontaneous annihilation of the LCO. This paper explores this interaction through wind-tunnel experiments using a variable-frequency disturbance generator to produce flow disturbances at frequencies near the inherent LCO frequency of an aeroelastic system with pitching and heaving degrees of freedom. The results show that incoming disturbances produced at frequencies approaching the LCO frequency from below produce a cyclic growth-decay in LCO amplitude that resembles interference between multiple sine waves with slightly varying frequencies. An aeroelastic inverse technique is applied to the results to study the transfer of energy between the pitching and heaving degrees of freedom as well as the aerodynamic power moving into and out of the system. Finally, the growth-decay cycles are shown to both excite LCOs in an initially stationary wing and annihilate preexisting LCOs in the same wing by appropriately timing the initiation and termination of disturbance generator motion.