As originally discussed, the felt is modeled as a nonlinear spring with a spring “constant” that increases as the compression of the spring increases. In this way, the spring stiffness constant is dependent on .
Because
and because the driving-point force on the mass and spring system is equal to , we can write
The above expression can then be written in terms of as
At any time in the model, the value of can be used to lookup or determine an appropriate value for the spring constant .