Thank you for your question and I understand your concern.
I do not have a clear understanding if you're referring to just the spin basket that spins or the spin basket and tub assembly. It is normal for the basket and tub to move freely up and down, left and right and forwards and back. If your washer is not sitting level and if one of the leveling legs is not supporting/touching the floor; the washer will shake and vibrate. Washing only one large garment can also cause it to shake/vibrate and could prevent the washer from reaching the fast spin because of an unbalanced load. The washer has dampeners/shocks attached between the bottom of the tub and the base and a couple of suspension springs suspending the tub assembly. I doubt if there is a problem with the springs and it's possible to have disconnect or broken shock/dampener but the main cause is likely the unit not sitting level and firmly on the floor.
I recommend checking and leveling the washer and then see how it acts. If you feel there is something wrong with washer I highly recommend calling a service technician to diagnose and repair your front loading washer.
You can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services