Ball speed on a rolling surface?

[enanthate]

A couple friends and I were brainstorming an idea today and thought of a way to make a pump using the waves in the ocean for energy.

So what it comes down to is say a 6cm i diameter steel ball in a tube, each side of the tube could have "pillows" that are part of a "membrane-pump". When the ball hits the pillow the impact force will cause it to pres sits contents out through the exit tube.

My problem is this... I'm having a hard time calculating the proper length of the tube that the ball will we rolling in.

We decided to say that the boat will rock back and forth 15 degrees on each side, so a total movement of 30 degrees. We also decided that it will take 3 seconds from one extreme bank to the opposite extreme bank.
'
How can we utilize a cosinus equation to decide the proper lengh of the tube? Too long and the ball willnever hit the sides. Too short and you won't get a good momentem to hit the pillows. Thanks in advance.

 

[enanthate]

Forgot to mention, Installed on a boat :D

 

[CWatters]

I suspect the optimum will be when the period of the wave is about the twice the time it takes the ball to go from one end to the other? I base this on the principle of resonance. An oscillating system absorbs the most energy from the source if the source frequency matches the resonant frequency.