Engineering
Cantilever Beam Deflection
y = P·x²·(3L − x) / 6EI

An end-loaded cantilever bows into a smooth cubic curve; increasing the tip load P scales the whole deflection profile, with the free end always dropping the most.
Computed & rendered in pure C# on the frozen OnlyCSharp 1.8 library — animation baked to GIF with the library's own
Gif encoder (no GPU, no ffmpeg, no external packages).