my waves professor is so funny
someone asked him why the models we use only work for small amplitudes and he said
"well, i'll demonstrate!"

then he started slowy sliding a tub of water back and forth harder and harder until it spilled all over the desk and on his clothes

"uh oh!!!!
... does that answer your question"

@imyxh Eh, that's somewhat misleading. There are things that break way earlier than at such a discontinuous transition: things become nonlinear (e.g. the pendulum's period being independent of amplitude is only true in small amplitudes).