Interesting idea, especially of a tank on a tower. The mass in the tank will change the natural frequency of the system. Probably going to be far from a linear relationship as there would be many factors involved.
If the tank was outdoors, the wind could excite the natural frequency or some kind of "thumper" could be used.
[Mandatory story] My group in a naval shipyard performed machinery condition / vibration analysis on rotating machinery (including some of that types of machines Ron was responsible for). When we had concerns about natural frequencies being close to a forcing frequency of a machine, we'd break out our 16 pound no-bounce (shot-filled) sledge hammer. A bump test on the machine will excite its natural frequencies. No lumberjack swings at the machine but just a gentle thud to make it vibrate.
One day the chief design engineer followed us out to a ship when we had to do a bump test. The machinist general foreman had called him, complaining we were beating on his machines with a sledge hammer, and he wanted to see for himself. We set up the tape recorder and accelerometers and hit the machine with out sledge hammer... with about a 4 inch swing. Thud.
"That's it? That's all you do?!?" the chief design engineer asked. Yep, not very exciting, is it?