The objective of this chapter is to discuss a very important issue of the effect of finite sampling with respect to either the finite length of the record or the finite sampling intervals. A few sampling theorems are discussed.

Here, we add damping to the harmonic oscillator, and explore the role of the resulting new time scale in the solutions to the equations of motion.Specifically, the ratio of damping to oscillatory time scale can be used to identify very different regimes of motion: under-, critically-, and over-damped.Then driving forces are added, we consider the effect those have on the different flavors of forcing already in place.The main physical example (beyond springs attached to masses in dashpots) is electrical, sinusoidally driven RLC circuits provide a nice, experimentally accessible test case.On the mathematical side, the chapter serves as a thinly-veiled introduction to Fourier series and the Fourier transform.

An exploration of the wave equation and its solutions in three dimensions.The chapter's mathematical focus is on vector calculus, enough to understand and appreciate the harmonic functions that make up the static solutions to the wave equation.