I did my training in a rental DA-20. A marvelous aircraft in most respects, but I had a couple of episodes of violent shimmy. Keeping the nose wheel light with aft stick seemed to help, but even then it would surface occasionally. Dunno how well the A&Ps kept up on preload, etc.

Early in my training, I was guilty of letting the nose wheel down too early after touchdown, which is the worst-case scenario.