Posted for bob mackey <n103md@yahoo.com>:

 I'm not familiar with the ES engine mount details, but on LNC2,
  shimmy could also be the result (or cause) of a cracked engine
  mount. So in addition to checking and possibly upgrading the
  oleo damper, you may want to consider inspecting the engine
  mount, or any other components that rigidly locate the nose gear
  relative to the airframe.