  We consider a one-dimensional cavity composed of two perfect, fixed mirrors
and a mobile membrane in between. Assuming that the membrane starts to move
from rest and that the membrane moves appreciably in a time-scale much larger
than the time-scale in which the cavity electromagnetic field evolves
appreciably, we derive simple analytic formulas that describe to good
approximation the evolution of the field and that provide an intuitive physical
picture. These formulas take into account the position, velocity, and
acceleration of the membrane and are valid for arbitrarily large displacements
of the membrane along the cavity axis. Also, we deduce the conditions under
which the field can be described to good approximation by a single
instantaneous mode.
