Coherent vibrations detected in optical experiments can offer insights into material properties and electronic interactions, but also yield complex time-dependent optical signatures, especially in hybridized systems. Here, we adapt techniques from studies on vibrational wave packets in molecules to analyze the optical signatures of coherent acoustic phonons in nanoparticles. This strategy enables us to better understand the implications of energetic changes induced by coherent phonons. We then apply this approach to systems that target coherent acoustic phonons as a route to modulate plasmon-exciton coupling and compare the results to theoretical calculations. Taken together, the described approach provides an intuitive, simple means of analyzing future systems and facilitates attempts to utilize, rather than simply observe, nanomaterial phonon modes.