Plain English Meaning
A motion that keeps swinging back and forth without getting smaller. It does not settle down on its own.
Full Definition
A repeating back-and-forth motion that continues at the same amplitude over time, with no reduction in size from one cycle to the next. In aircraft dynamics, it describes a disturbance that, once started, keeps oscillating at a constant magnitude rather than dying out.
Context Anchor
Seen in aircraft structure, control system, and vibration discussions when describing motion that does not die out on its own.
Derivation
From the prefix 'un-' meaning 'not', and 'damped', from Middle Dutch 'dampen' meaning 'to deaden' or 'to suppress'. So 'undamped' literally means 'not deadened' -- the motion is not being suppressed or reduced.