Having gone through the theory behind oscillations and simple harmonic motion, we are now able to apply our knowledge to practical situations. This SparkNote draws upon the equations and concepts already established, developing a more complete understanding and the ability to apply our knowledge of oscillations and harmonic motion. We take an empirical approach to oscillations in this section, starting with a given physical system and finding the equations that govern its oscillation.
We begin by examining various physical situations in which simple harmonic motion arises, including the torsional oscillator and the pendulum. We then examine the quite surprising relationship between simple harmonic motion and uniform circular motion. Finally we begin to tackle the topic of complex harmonic motion, looking at both forced and damped harmonic motion. Unfortunately, a full treatment of complex harmonic motion requires far too complex mathematics, so we will treat these topics in a primarily qualitative manner, simple stating the equations when necessary. Complex harmonic motion is most common in practical use, however, and the study of it will be easily applicable to a variety of situations.
With this SparkNote we conclude our study of classical mechanics. Having studied the concepts behind linear, rotational, and now oscillatory motion, one can describe almost any mechanical situation.