We have already studied the most common types of motion:
linear and rotational
motion. We have developed the concepts of
work,
energy, and
momentum for these types of motion. To
complete our study of classical mechanics we must finally examine the
complicated case of oscillations. Unlike the other types of motion we have
studied, oscillations generally do not have constant acceleration, are many
times chaotic, and require far more advanced mathematics to handle. As such, we
give the most complete treatment to the subject as possible, concentrating on
the kinds of oscillations that are easiest to examine.

We begin be defining oscillations, and
the variables associated with this motion. Next we take a closer look at a
special kind of oscillation, simple harmonic motion. It is this kind
of oscillation that will form the bulk of our study of oscillations. We derive
the motion of simple harmonic systems, and relate this motion to the concept of
oscillation that we have already defined. This derivation is quite complex, and
to complete it we must use some complex calculus. The derivation itself is not
as important as the end product, but if one can understand the mathematics, it
can greatly increase understanding of the topic.

Deriving the equations for simple harmonic motion will allow us to take an in
depth look at various kinds of harmonic motion, as seen in the next section.