The damped harmonic oscillator physics problem is a standard oscillation problem in calculus physics for pre-engineering students in a community college. The use of alternative linear algebra eigenvalue stability method is consistent with the upper engineering courses using control theory. The external force and friction damping would become the control and feedback respectively in control theory. The objective of quantifying stability has wide applications from Lego to Arduino driven educational robotic systems in mechanical engineering student projects. The IllustrisTNG galaxy simulation data and the Skynet Robotic Telescope Network Supernova data are also open-source data for student projects taking on the stability studies. The equity of authentic experience in the outcome of each student would require differential-unequal input conditions across the cohort of students every year. An extension to oscillation without physics is mathematically justified when the studied system could be represented as two coupled linear first order differential equations. All the teaching contents were extracted from the open sources posted on the websites of leading university professors and professionals. The eigenvalue pedagogy is also ready for the online delivery of student skill learning projects in the post-COVID era, given a community college setting. The assessment has been conducted with the what-if critical thinking perspective. The sustainability of the eigenvalue pedagogy in community college student skill learning projects in the post-COVID era is discussed, together with this transfer-enhancement pedagogy. Recommendations are presented. [For the full proceedings, see ED671809.]