This paper brings the theory into the laboratory. If inertia emerges from interaction with a substrate, its response should not be strictly instantaneous. Every physical medium has a relaxation time — a memory. Why should inertia be different? This work explores that possibility: inertial mass may depend not only on instantaneous acceleration, but also on how acceleration changes over time. Under ordinary conditions the effect would be imperceptible. But in high-precision experiments — atom interferometers, torsion balances, mechanical resonators — even extremely small deviations can be detected. The central idea is simple but powerful: if inertia is emergent, it must leave a dynamical signature. The paper shows that this signature appears as a slight frequency dependence in inertial response. At low frequencies everything looks standard. But with increasing precision or modulation, a subtle inertial “memory” may emerge. For the first time, a framework originally motivated by galactic dynamics is brought into the laboratory — not as cosmological speculation, but as a measurable prediction.