If you add weight to the moving structure of the sub you will lower the Fs since the weight in motion allows the cone to move to its peaks easier. The drawback is you need to add motor strength to compensate to control the moving mass in turn raising the Fs back up. Vicious circle?
I think we've established that "Ka Ka" and "Tukki Tukki" don't work.
It wouldn't do much to change the Fs of the speaker, but it would keep the basket from resonating. I haven't heard of any designs that were this weak however. Umm... I really don't know what you are trying to achieve
All a basket does is hold the assembly together. In some applications it can be utilized for additional thermal management instead of using a proper cooling design (moving air) to begin with. In the case of a really thin stamped steel frame you may get some ringing through the basket which can color the sound or cost the driver some moving energy.
I think we've established that "Ka Ka" and "Tukki Tukki" don't work.
