Gerard,
In general, a popular vibration inducer on the 360 is the nose gear door.  If the trailing edge is not snug up against the fuselage, it can vibrate at high speed (>200 KIAS).  For vibration at any air speed, in particular vibration tied to engine speed, look for signs of contact between engine parts and cowling/air frame parts.

Chris Zavatson
N91CZ
360 std
www.N91CZ.com