  We consider the description of classical oscillatory motion in ZM theory, and
explore the relationship of ZM theory to semi-classical Bohr-Sommerfeld
quantization. The treatment illustrates some features of ZM theory, especially
the inadequacies of classical and semi-classical treatments due to
non-analyticity of the mapping of classical trajectories onto the ZM clock
field. While the more complete ZM formalism is not developed here, the
non-analyticities in the classical treatment resemble issues in the comparison
of classical and quantum formalisms. We also show that semi-classical
quantization is valid for a periodic manifold in ZM theory, though the quantum
number $n=0$ is allowed, as it would be in quantum mechanics for a periodic
manifold. Still, this suggests a connection to the first-order success of Bohr
theory in describing the phenomenology of atomic quantum states. The
approximate nature of the semi-classical treatment of three dimensional atomic
orbits is, however, also apparent in relation to ZM theory. These observations
are preliminary to a discussion of ZM theory in relation to quantum mechanics
and quantum field theory in subsequent papers.
