The harmonic modulation of coherent systems gives rise to a wealth of interesting physical phenomena, e.g., the AC-Stark effect and Mollow triplets, with important implications for coherent control and quantum frequency conversion. Optomechanical systems enable access to extreme driving conditions by exploiting their high oscillations frequencies and long temporal coherence. Here, we experimentally demonstrate a novel regime of temporal coherence in oscillators harmonically driven at extreme energy modulation amplitudes, which is characterized by temporal correlations with time-scales much shorter than the modulation period. These arise from accelerated energy changing rates during the harmonic cycle and manifest themselves as comb of spectral resonances, termed the acceleration beats, with energy scale tunable by the energy modulation amplitude. We provide experimental evidence for the acceleration beats by modulating a confined exciton-polariton Bose-Einstein condensate (BEC) using an acoustic wave. The detection of the beats is underpinned by the high sensitivity of the BEC energy to the acoustic driving field, which simultaneously preserves the high BEC temporal coherence. The acceleration beats are a general feature associated with accelerated energy changes: analogous features are thus also expected to appear under highly accelerated motion e.g., in connection with Cherenkov and Hawking radiation.