The solutions to the coupled heave and pitch equations are found using the method described by Bhattacharyya (1978) which is outlined below:

If additional damping for heave and pitch has been specified, then it is applied at this point.

 this is the tuning factor

The specified non-dimensional damping, , is assumed to be evenly distributed along the length thus the additional damping terms (given the superscript +) are defined as:

and