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
Related Videos:
Hyperbolic Functions: Catenary: Example 1: Reverse Proof:
Hyperbolic Functions: Catenary: Formula and Proof:
Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: .
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@spaminator Hey, can you please remove the downvotes on my comments? I comment on my posts to include links and upvote the comment to serve as a "Pinned" comment, much like YouTube.
@mack-botjr please stop downvoting my replies to @spaminator...
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Thanks for info, very excellent my friend @mes
Resteem...
explanations that are easy to understand @mes
I don’t always graph catenaries but when I do I illustrate the physics behind it by pulling a string 😉
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-hyperbolic-functions-catenary-example-2-graphing-catenaries
@spaminator Hey, can you please remove the downvotes? I comment on my posts to include links and upvote the comment to serve as a "Pinned" comment, much like YouTube.