have you tried to research this on your own ?
a quick google for "landing gear shimmy" found lots of hits, including one with ...
"Shimmy is an oscillation in aircraft landing gear that can occur both on landing and take-off, typically in a band of velocities. It causes excessive wear on components and can cause accidents. The nose wheel is roughly like a caster on a shopping trolley: the horizontal axle of the wheel is mounted in an assembly that is free to rotate about a vertical axis. Shimmy is (or at least includes) oscillation of the wheel assembly about this vertical axis. The current engineering approach has little understanding of the physical mechanisms causing shimmy, but relies on the use of shimmy dampers, and on systematic maintenance and replacement of landing gear components."
hope that helps your assignment ...