when it is restrained from motion and subjected to regular waves. The forces acting on the body are: The Froude–Krylov force, which is the pressure in the undisturbed waves integrated over the wetted surface of the floating vessel. The Diffraction forces, which are pressures that occur due to the disturbances in the water because of a body being present. Finding the forces on the ship when it is forced to oscillate in still water conditions. The forces are divided into: Added mass forces due to having to accelerate the water along with the ship. Damping (Hydrodynamic) forces due to the oscillations creating outgoing waves which carry energy away from the ship. Restoring forces due to bringing the buoyancy/weight and moment equilibrium out of balance. In the above, "Ship" must be interpreted widely to also include other forms of floating structures. The obvious problem in the above method is the neglection of viscous forces which contribute heavily in modes of motion like surge and roll. On a computer the above algorithm was first introduced by using strip theory and Boundary Element Method. Today both of the methods are still used if the need for fast calculations outweigh the need for precise results and the ship designer knows the limitations of strip theory. More advanced programs that are used today utilizes Boundary Element Method through different applications (such as WAMIT, SESAM WADAM, MOSES, NeMOH and ANSYS AQWA) some may also include the effects of viscosity. The insight into the forces that governs the seakeeping behavior of a ship gained from the above are of course still valid within considered limits of free surface linearity. Calculating the RAO The RAO is a transfer function that is only defined when the ship motions can be assumed to be linear. The above forces can then be assembled into an equation of motion: Where is a rigid body motion such as heave, is the oscillation frequency, is the structural mass and inertia is the added mass (frequency dependent), is the linear damping (frequency dependent), is the restoring force coefficient (stiffness matrix) and is the harmonic excitation force proportional to the incoming wave . Here is the wave amplitude. If we assume this can be solved for and the RAO is then: where is the linear excitation force complex amplitude per wave height. The RAO is a frequency dependent and complex function (the in the above expression