Question

Why is there a discrepancy between the rubber band spring constants derived via the simple harmonic motion and the hanging-mass methods?

Answer 1

Rubber band does not have a linear spring constant like real helical spring. If the band is added weight it is likely to be non-linear in the beginning and may become linear with higher weights.

Thus in the linear region we can measure spring constant by hanging mass method.

In contrast when you try to replace spring with rubber band, we can not get simple harmonic motion , since we do not get restoring force which is proportional to compression on Band in slack position . In fact when extended rubber band contracts to mean position , it will get no compressive force at all , unlike a spring. Hence Oscillations are not feasible at all.