Interesting physical phemomena to model

Question

I'm a high-school student looking for some interesting physical problems to model. Some examples include the shape a trampoline makes when you jump on it, the equations describing heat transfer, collisions of particles (something like 3Blue1Brown's video on "How many collisions?" where Pi pops up unexpectedly).

I'm particularly interested in how differential equations can model these scenarios, such as heat transfer. Do you have any good problems you can share?

Answer 1

The Furuta pendulum is a classic example in control theory and it can be interesting if you want to model physics problems

https://en.wikipedia.org/wiki/Furuta_pendulum