Oscillayne: Harmonic Pulse / Waveform Resonance

Optics, Waves & Sound arc, page 110 of 193. Back to The Pixelated Physics Universe

Who they are

Push a swing at just the right moment and it climbs higher each time. Resonance: drive a system at its natural frequency and small pushes build into large oscillations. Oscillayne personifies it. Oscillayne wears it in pixel art on a unisex tee.

Oscillayne is a character of the Optics, Waves & Sound arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

A damped oscillator driven by a periodic force responds most strongly when the drive is close to its natural frequency. The less damping there is, the taller and narrower that resonance peak becomes, which is how small, well-timed pushes build up large swings.

$$ \begin{gathered} \ddot x + \gamma\dot x + \omega_0^{2}x = \frac{F_0}{m}\cos\omega t \\ A(\omega) = \frac{F_0/m}{\sqrt{(\omega_0^{2}-\omega^{2})^{2} + \gamma^{2}\omega^{2}}} \end{gathered} $$

Symbol Meaning SI unit
$x$ displacement m
$\gamma$ damping rate s⁻¹
$\omega_0$ natural angular frequency rad/s
$F_0$ driving force amplitude N
$m$ mass kg
$\omega$ driving angular frequency rad/s
$A$ steady-state amplitude m

Sources

Crossovers

Oscillayne meets Sloshwyn (Coffee Sloshing 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.

Oscillayne meets Rijka (Singing Heat). Rijka's pipe sings because the heated gauze adds heat in step with the sound, feeding energy into the acoustic mode. It is Oscillayne's resonance driven by heat instead of a push.

Wear the lore

Concept keywords: Harmonic Pulse / Waveform Resonance, Oscillayne, Optics, Waves & Sound, physics lore, Pixelated Physics