Aqwa solves a set of linear algebraic equations to obtain the harmonic response of the body to regular waves. These response characteristics are commonly referred to as response amplitude operators (RAOs) and are proportional to wave amplitude.
The set of linear motion equations of 
hydrodynamic interaction structures with frequency dependent coefficients
are obtained as:
 | (4–49) |
where 
is a 6M×6M structural mass matrix, 
and 
are the 6M×6M hydrodynamic added mass and damping matrices including the hydrodynamic
interaction coupling terms between different structures, 
is the assembled hydrostatic stiffness matrix of which each diagonal
6×6 hydrostatic stiffness sub-matrix corresponding to individual structure is defined by
Equation 3–19, and all off-diagonal 6×6 sub-matrices are null as
there is no hydrostatic interaction between different structures.
Equation 4–49 can alternatively expressed as
 | (4–50) |
where
is termed the transfer function or modal receptance which relates input forces to output response.
In addition, Aqwa can calculate the RAOs at any point of the structure given the RAOs at the structure's center of gravity and the vector from the center of gravity to the position of interest. The RAOs of a point P of (Xpm , Ypm , Zpm )T on the m-th structure may be found using the following relationship
 | (4–51) |
where the translation matrix between the center of gravity (Xgm , Ygm , Zgm )T and the point P is
