Diagnosis
That's an imbalance issue. The washer's self-balancing system (called the Perfect Balance system on Maytags) is being overwhelmed, usually because the washer isn't level, the load is uneven, or the shipping bolts weren't removed.
How to Fix It
Let's get it stable. 1) First, confirm all four shipping bolts are removed from the back of the washer. If they're still in, the inner tub is locked and will vibrate violently. 2) Use a carpenter's level on top of the washer (front-to-back and side-to-side). Adjust the leveling legs by turning them clockwise to raise or counter-clockwise to lower. The washer must be firm on the floor – no rocking when you push on the corners. 3) Ensure the washer isn't touching the wall or any cabinets. You should have a couple inches of clearance all around.
If That Didn't Work
The suspension system – the four rods and springs that hold the inner tub – might be worn or damaged. Open the lid and press down firmly on opposite sides of the drum. It should have firm, even resistance and rebound smoothly. If it's sloppy or clunks, a suspension rod might be broken.
Heads Up
A concrete floor is best. If it's on a weak wooden subfloor, the flexing of the floor itself can amplify the vibration. In that case, consider placing a thick, solid rubber pad (made for appliances) underneath it to dampen the movement.