The harmonic oscillator is everywhere
Why one differential equation shows up in pendulums, circuits, molecules, and quantum fields — and why nature had no choice.
Aug 2, 2026physics
Hi — I'm Nihad.
I write software for a living and study things for the joy of it — physics problems, mathematics, philosophy, economics, puzzles. This site is where all of it lives in one place: the projects and the writing, technical and otherwise.
The pages here shift with their subject — physics reads off a chalkboard, essays sit on warm paper. Wander around.
Problem of the moment
The falling chain
A chain is folded in half and hung so one end is fixed and the other is free to fall. As the free side falls, does its tip accelerate faster than g? (It does — but convincing yourself with momentum flux, not energy hand-waving, is the fun part.)
chewing on it since 2026-08
Recent
Brachistochrone racer
An interactive simulator racing beads down curves — straight line vs. circular arc vs. the cycloid that beats them both.
Jul 28, 2026physicscs
Generating functions: a clothesline for numbers
How hanging a sequence on a power series turns recurrences into algebra — with Fibonacci as the demonstration.
Jul 14, 2026math
Berkeley's master argument, and why it fails beautifully
The bishop's one-move checkmate against mind-independent objects — and the quiet equivocation that undoes it.
Jun 21, 2026philosophy
The inverse sprinkler, worked through
If a lawn sprinkler sucks water in instead of spraying it out, which way does it turn? A worked solution with momentum accounting done honestly.
Jun 5, 2026· worked problemphysics