Barge excursion time series graph

You are saying that when you input a regular wave with y period you expect the vessel to also have a response with y period?
In the above plot "Excursion (x)" is in the global x direction? And can be interpreted as surge?

Dear georgina,

Firtsly, thanks for answered my question.

Yes, that's the point.
As I know, vessel respons (surge, sway, heave) period are considered by wave period.
For example, 10 period wave will generate 10 period respon also.

Thanks for helping.

If it were only that easy. A motions analysis is determining the mass, stiffness, and damping matrix and then making the equations of motion. You can think of all these calculations being needed for a transfer function. The real and imaginary part need to be solved. The force from the waves is used as input to the transfer function. It is very rare that a wave period will generate exactly the same period in response.

In regular wave using, the equation of motion could directly determine by wave force as input without transfer function. I'd done a simulation with regular wave but the results (motion period) are different to with wave period.
On surge and sway motion, there is an influence of mooring.
Could you explain how mooring affect to those motion period ?

Have you done a mass on a spring and dashpot problem lately?
The mooring system influences all 6 degrees of freedom. That is the reason mooring systems are added.
Mooring systems change the spring (stiffness) and the dashpot (damping) of the system.
Please review a vibrations textbook before submitting another question.