What Jhiemnga said...…...Loose parts/excessive play in the strut/scissors link bushings, bolts, etc., or a bad worn out shimmy damper. Or, badly worn or out of balance nose tire. Any or all could cause nosewheel shimmy. Sounds like when you landed the plane, you were better at holding weight off the nose during the rollout than the other fliers. Often, as instructor, when the flying student allows the nose to "wheelbarrow" too much during landing, a quick pull aft on the yoke to reduce weight on the nose will stop the vibration. Then at slow taxi speeds, the shimmy may not be evident. A 206 is quite a bit heavier in front, as is a 182, especially if the pilot is transitioning from, say, a lighter-handling 172. I'd have a mechanic check out the nose gear for wear and/or (hopefully not!) more extensive damage, firewalls have been known to get bent from nosewheel-first landings in 182s and 206s.