# Fit the Linear Terms in the Model

The purpose of this fitting is to determine the overall shape of the dynamic stiffness and phase angle curves.

- The results from Initial Design Parameters are used as the starting point.
- You can observe from the plot below that the model is linear in terms of the
parameters k
_{0}, k_{1}, k_{2}, c_{0}, c_{1}and c_{2}. Non-linearity occurs in the parameters p_{0}, p_{1}, p_{2}, q_{0}, q_{1}and q_{2}. Therefore, p_{0}, p_{1}, p_{2}, q_{0}, q_{1}and q_{2}are kept fixed at reasonable values as an optimization is run to determine k_{0}, k_{1}, k_{2}, c_{0}, c_{1}and c_{2}. - Since the model is linear when parameters
p
_{0}through q_{2}are fixed, it does not show any amplitude dependency. Moreover, the equations can be solved using linear methods. - The following plot shows the effect of a linear fit: