The TPU output had 5% damping at 5 Hz

Here is the same model, but with a Linear Material E = 41 MPa instead of a Hyperelastic Material.

Increased E to 90 MPa and now the flat part of the curve is about 1.22 N which is where the TPU was.

This requires about the same 0.125 kg mass, but when the Modal solution is run, the natural frequency is 11.6 Hz.