Positive feedback loops cause small displacements from equilibrium to grow exponentially, often with catastrophic effects. This demonstration with a sound system is just one example. This topic is especially relevant today to the understanding of how "climate change" can become "climate catastrophe."
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https://www.youtube.com/watch?v=BzqitY3nC7A
This is a bonus topic for a calculus lesson on derivatives of inverse trigonometric functions. It turns out that such a derivative is part of the calculation of the angle of a rainbow. This bonus lesson is a nice mix of physics and mathematics. The graphics in this lesson are generated using Geogebra, which is available from Geogebra.org.
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http://mathwithoutborders.com
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https://www.youtube.com/watch?v=Lim7KbKT2zU
3-D demonstration of the motions of the sun and moon in the sky, created using Visual Python (VPython).
[By the way, given the number of clueless comments, it seems I must point out, this simulation HAS ABSOLUTELY NOTHING TO DO WITH THE MIND NUMBINGLY LUNATIC FLAT EARTH "THEORY" NONSENSE!!! (Don't waste my time.) This is about the apparent sky for a localized observer: a phenomenological perspective one has for observational astronomy or navigation. (Go outside and look up!) When you stand on the ground and see a few hundred yards, the earth appears locally flat. You lack depth perception for cosmic distances because your eyes are close together compared to the distances involved. That's why the sun, moon, and stars appear to be at the same distance. When everything in the cosmos appears the same distance away, it gives the illusion that they all lie on a sphere centered on the observer. Hence the sphere of the sky is an illusion. This simulation is about understanding this localized perspective.]
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https://www.youtube.com/watch?v=5k--My8fnes
This is part of a series of arithmetic lessons created for my grandkids, but I'm opening them to the world. You can access an annotated index with links on my Math Without Borders website here: https://mathwithoutborders.com/the-grandpa-project
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https://www.youtube.com/watch?v=eNkYf1OZ3WY
The video introduces the concept of instantaneous rate: the derivative, which is one of the fundamental ideas in calculus.
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https://www.youtube.com/watch?v=_tjeyM9CD-A
This is part of a series of arithmetic lessons created for my grandkids, but I'm opening them to the world. You can access an annotated index with links on my Math Without Borders website here: https://mathwithoutborders.com/the-grandpa-project
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https://www.youtube.com/watch?v=h2YSDT3biP8