2000 Mercury Marquis shimmy

Suspension problem
2000 Mercury Marquis V8 Two Wheel Drive Automatic

car shimmies at 40mph only sometimes goes away but comes back sometimes it comes and goes
only at 40mph cruse at 40 it shimmies over 40mph
goes away under 40mph goes away but sometimes
it is gone at 40mph this is not a constant problem
there is no noise typical of a universal joint.
this is driving me nuts can not pin point the problem