How to isolated stand from springy floors?

If you have access to the basement and it is un finished, you could put in some "lally columns" see link
http://www.lowes.com/pd_210155-46417-P+M204_0__?productId=3201387
I did this when I had an LP12 to reduce the springy response to footfall. Locate the two joists that your equipment rack is supported by and tighten the lally columns to just touch the joist. Then the solid cement floor is transferred through the columns and acts like a foundation to support the floor.
Caution though, if you have expansive soil in your area this will not work.
Another partial solution if you have access is to add "bridging" between the joists. This is a board that fills that gap in a perpendicular position to reduce the flexing that takes place when a joist deflects from load.

As a final note, and not to argue with Elizebeth, but I think adding weight will just prove to further damage to the floor and cause more issues down the road. But that is just my opinion and I am not an engineer.

What Theo mentions about supplementary posts is a good call if possible, because it's likely the most effective. Bridging will help as an alternative, but along similar lines would be to sister additional joists on either side of the joists where the load lies. Even if you basement is finished, this is not a hard job and cosmetically we're talking some drywall work and paint (both cheap). Of course, if you have wiring / plumbing through existing jiosts, that does add complication.

A floor should be able to hold furniture and other heavy and heavier items than just loads of send-boxes recommended by Elizabeth. Further damage will continue to the unloaded springy floor that needs to be damped.

Mass on a spring isolation. Like the pros use.

I concur with Elizabeth, but suggest using dumb-bells instead of bricks since they are relatively easy to find and install. They also provide a more effective way to accumulate mass compared to bricks.

The ones to look for are Hex-Shaped with a Rubberized Covering. 4 50-lbs bells arranged in parallel, with a 1/4 or 1/2 inch Marble Tile placed on top should provide a fairly even surface to put your stand.