Hyperbolic Functions: Catenary: Example 2: Graphing Catenaries

Math Easy Solutions

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In this video I go over further into Hyperbolic Functions and this time graph a family of catenary curves to analyze their behavior. Recall from my earlier videos that I proved that a cable hanging by its own weight across two heights is described with the hyperbolic function, y = c + a cosh(x/a), and is known as a catenary. I use the Desmos Online Graphing Calculator to plot out the catenary function for varying values of a and c. Given that a is greater than 0, as ‘a’ increases the curve becomes flattened, which is expected since ‘a’ is proportional to the tension within the hanging cable. This can be visualized by pulling a string in which the harder you pull the more flat the string becomes. This is a very interesting video on not only graphing catenaries but also on some of the physics behind them, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvpWyKvW5m604Mi9vQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-hyperbolic-functions-catenary-example-2-graphing-catenaries