Mass Spring System Project Reflection
The final assignment for Trigonometry 1060 required graphing the cycle of a spring with a mass attached to it. It involved multiple concepts covered in class, such as the graphs of Sine and cosine, transformations, identities and their proofs, the unit circle, Pythagorean Theorem etc. One advantage of this project was applying these concepts to real life situations, which provide a useful insight of the common place trigonometry has in everyday life.
For example one of the most common spring systems that can be found is a hanging scale, which is often used in grocery stores or in portable versions to weight luggage; it follows the same principles as this project and it is critical to understand the period, amplitude and frequency of what happens in the system to accurately display the corresponding weights on a readable scale for the user.
Another very useful application of trigonometry involves music amplification for example. Sound waves are always graphed using sine and cosine functions, and the amplitude and frequency determine the pitch and volume of the waves; it helps to draw polar graphs of microphone pickup patterns which usually include the cardioid and hyper cardioid shapes. And it also plays a vital role in synthesizers which rely on different sine waves and their variation to produce even the most uncommon or unthinkable sounds.
More recently, trigonometry has become more personal, as I have worked at Lens Crafters manufacturing prescription lenses. The prescription depends on the angles at which light enters the lens. It also allows us to transcribe prescriptions and to use the correct curvatures to achieve the optimal optical center. A majority of the machines we use have springs that allow movement of certain parts in order to achieve their desired motion and function.
