Sloshwyn: Coffee Sloshing Resonance
Mechanics, Chaos & Fluids arc, page 101 of 193. Back to The Pixelated Physics Universe
Who they are
Sloshwyn has one line, and says it often: “Walk slower than the slosh resonance.”
Sloshwyn is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Walking with coffee spills because gait frequency is near the liquid's sloshing frequency.
$$ \begin{gathered} \omega_{mn}^{2} = \frac{g\,\xi_{mn}}{R}\tanh\!\left(\frac{\xi_{mn} H}{R}\right), \qquad \xi_{11} \approx 1.841 \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\omega_{mn}$ | sloshing natural angular frequency | rad/s |
| $g$ | gravitational acceleration | m/s^2 |
| $\xi_{mn}$ | n-th zero of J_m' | — |
| $R$ | cup radius | m |
| $H$ | liquid depth | m |
Sources
Crossovers
Sloshwyn meets Oscillayne (Harmonic Pulse / Waveform Resonance). Sloshwyn spills coffee when walking near the liquid's sloshing frequency. Oscillayne knows why: driving a system near its natural frequency builds up large oscillations.
Sloshwyn meets Ringward (Q Factor Resonance). Sloshwyn's coffee is a lightly damped oscillator. Ringward measures how lightly with Q: the higher the Q, the more cycles it rings and the bigger the resonant response.
Sloshwyn meets Whirlda (Euler's Disk). Sloshwyn's coffee rings down as damping takes its energy. Whirlda loses energy too, but as she does, her wobble rate rises, heading toward a finite-time singularity that real contact physics cuts off before it arrives.
Wear the lore
Concept keywords: Coffee Sloshing Resonance, Sloshwyn, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics