Two types of periodic and transient motions of large woodpeckers are considered. A drumming woodpecker may be modeled as a harmonic oscillator with a periodic forcing function. The transient behavior that occurs after the forcing is turned off suggests that the double knocks of Campephilus woodpeckers may be modeled in terms of a harmonic oscillator with an impulsive forcing, and this hypothesis is consistent with audio and video recordings. Wingbeats are another type of periodic and transient motion of large woodpeckers. A model for the flap rate in cruising flight is applied to the Pileated Woodpecker (Dryocopus pileatus) and the Ivory-billed Woodpecker (Campephilus principalis). During a brief transient just after taking off, the wing motion and flap rate of a large woodpecker may not be the same as in cruising flight. These concepts are relevant to videos that contain evidence for the persistence of the Ivory-billed Woodpecker.