A rapid spin cycle is actually a GOOD thing. This is an indication that the gearcase (transmission) and the drive motor are both running strong.
If the washer shudders during the spin cycle the first thing you need to do is check to ensure the washer is properly leveled. The following link explains:
The model Whirlpool top loader you have, has an auto-leveler mechanism on the back two legs that can become unlevel periodicailly. You should check the washer level from time to time when it is empty. You need to also make sure the washer is level in ALL directions (front-to-back and side-to-side).
Accidental unbalance problems that can occur from washing blankets, comforters, or heavy loads of towels can also cause the washer to become unlevel and shake. This can also contribute to the level mechanism becoming unbalanced.
Overloading the washer can also cause unbalance problems. Washing blankets or conforters can cause the load weight to shift to one side of the tub. This will result in a tub that shakes violently and bangs against the cabinet. You may have to redistribute the load weight when washing heavy items. This can also occur when washing loads of towels. This is NORMAL as some heavy items do not distribute the weight evenly.
Another problem (which is less common) that can contribute to wash unbalance problems is a weak floor under the washer. If the floor flexes (even the slightest) during the spin cycle, it can cause the washer to bounce or shake. Mobile homes or laundry rooms on the second floor of a home are notorious for having weaker floor structures. This washer has a 35 gallon tub capacity. Coupled with the weight of a wet load and the spinning action, this can put a lot of centrifugal force on a floor.
If you have any questions or concerns, please post back and let me know. I hope this information is helpful to you.