Run Detail
completedgemini-4-hydrogenRecorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
Batched — not timed
Total Tokens
38,929
Input Tokens
1,372
Output Tokens
37,557
Reasoning Tokens
29,993
Reasoning Effort
default
Est. Cost
$0.1419
Started
11/12/2026, 6:56:29 PM
OR Provider
Google
Finish Reason
stop
Generation ID
gen-batch-1794509791-5f8cd757d6a7995f9a97
Turns (1)
Turn #1
1,372 in37,557 out29,993 reasoning38,929 total
user
You build physics demonstrations for a science museum. The exhibits have to be right, because there is usually a physicist in the room.
Build me the falling slinky.
The exhibit
A single HTML page. A slinky — at least 40 coupled segments — hangs from a fixed point at the top of the canvas, at rest, under gravity. Then it is released.
Controls:
- Release — lets go of the top. Reset — hangs it back up, at rest.
- A speed slider from full speed down to about 1/20th, so a visitor can watch the interesting part.
- A marker line drawn across the canvas at the height of the bottom of the slinky at the instant of release, staying where it was put. Visitors need something to compare against.
- A running clock in milliseconds since release.
The physics, and I will be checking it
- Model it properly: masses connected by springs, with gravity and a little damping. Hooke's law between neighbours, integrated over small time steps.
- The hanging state must be the true equilibrium. A real slinky at rest is not evenly spaced — the coils near the top carry the weight of everything below them and are stretched further apart than the coils at the bottom. Your initial condition must have this. Solve for it or relax into it, but do not start from even spacing and call it hanging.
- The integrator must be stable at the stiffness you choose. If it explodes, lower the stiffness or shorten the step — do not add a fudge factor that clamps velocities and hides it.
- No scripted behaviour. Every segment obeys the same rules. Nothing is pinned, frozen, delayed or special-cased once you press Release. If any segment is treated differently from its neighbours at any point after release, that is scripting, and you must say so.
House rules
- One file. Everything inline — no CDN, no external stylesheet, font, script or image.
data:URIs are fine. - No libraries. No physics engine.
- No network at runtime.
- No
localStorage,sessionStorage, cookies orindexedDB— sandboxed frame, they throw. - Return the file as exactly one fenced
htmlblock.
Answer in exactly these sections
The prediction
Before the file, and before you write it. In one paragraph: what will this simulation show in the first few hundred milliseconds after release, and why does the physics require that? Be concrete about what each end of the slinky does and roughly when.
Commit to this. It is the claim I am going to test your simulation against.
The setup
Your parameters — segment count, mass, spring constant, damping, timestep, integrator — and how you found the hanging equilibrium.
The file
The single fenced html block.
What it actually shows
Now be honest. Having written it, does the simulation reproduce what you predicted?
Say plainly if it does not. Say if you are unsure. Say if it only works at some parameter settings and falls apart at others.
Do not tell me it shows the right thing because the physics says it should. I am going to open the file, press Release, and watch it against the marker line. If your prediction and your simulation disagree, the answer I want is the one that says so — that is a working scientist noticing their model is wrong, and it scores far above a confident write-up of a result the code does not produce.
assistant
The prediction
In the first ~330 ms after release, the top end of the slinky will drop rapidly and collapse coil-by-coil into a dense falling bundle, while the bottom end will remain motionless right on the marker line until roughly 320–340 ms, at which point the collapsing bundle reaches the bottom and the entire slinky falls together under gravity. Physics requires this because before release, the bottom mass is in static equilibrium between its downward weight and the upward tension of the bottom spring, and after release no information about the vanished top support can reach the bottom until a mechanical wave travels down the chain; in a slinky whose coils stack upon contact rather than passing through one another, a nonlinear compression shock sweeps downward from the released top (accelerating initially at $61g$ as it loses its $60$-segment support) and overtakes the slower linear elastic relaxation wave (which would take ~566 ms to reach the bottom), arriving at the bottom in the shock-collapse time $t_c \approx \sqrt{2 \Delta H / (3 g)} \approx 329\text{ ms}$, with the whole slinky then continuing downward past the marker line (with a slight longitudinal rebound after full collapse).
The setup
- Segment count: $S = 60$ spring segments connecting $N = 61$ point masses ($i = 0$ at the top, $i = 60$ at the bottom).
- Mass: $m = 0.004\text{ kg}$ per node (total mass $M = 0.244\text{ kg}$), with $g = 9.81\text{ m/s}^2$.
- Spring constant & rest length: $k = 45.0\text{ N/m}$ per segment in tension ($d \ge L_0$, giving an effective overall slinky stiffness of $k/S = 0.75\text{ N/m}$), with unstretched coil spacing $L_0 = 0.0025\text{ m}$ (unstretched stacked height $L_{\text{un}} = 0.150\text{ m}$). For coil contact ($d < L_0$, preventing coils from passing ghost-like through one another), a stiffer Hooke contact spring $k_{\text{contact}} = 9000.0\text{ N/m}$ ($200k$) is used symmetrically on every segment.
- Damping: Internal linear velocity damping $c = 0.025\text{ N}\cdot\text{s/m}$ between adjacent masses ($\zeta \approx 0.029$ in tension), plus $c_{\text{impact}} = 3.6\text{ N}\cdot\text{s/m}$ when coils are actively compressing in contact ($d < L_0$ and $v_{j+1} - v_j < 0$, giving $\zeta_c \approx 0.30$ without sticky tension on rebound).
- Timestep & integrator: Classic 4th-order Runge–Kutta (RK4) with fixed substep $\Delta t = 50,\mu\text{s}$ ($0.00005\text{ s}$), well inside the RK4 stability limit for the contact frequency ($\omega_c \Delta t = 2\sqrt{k_{\text{contact}}/m},\Delta t = 0.15 \ll 2.83$).
- Hanging equilibrium: Solved analytically from the bottom mass upward so every interior mass has identically zero net force at rest. Segment $j \in {0,\dots,S-1}$ supports the $(S - j)$ masses below it, giving exact equilibrium spacing $d_j = L_0 + \frac{(S - j)mg}{k}$ and total hanging length $H = S L_0 + \frac{S(S+1)mg}{2k} = 1.74576\text{ m}$ ($\Delta H = 1.59576\text{ m}$). On Release, the constraint on mass $0$ is simply removed; every mass obeys the exact same force law and integrator.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Falling Slinky — Physics Exhibit</title>
<style>
:root {
--bg: #0b1120;
--panel: #111827;
--border: #1e293b;
--text: #e2e8f0;
--muted: #94a3b8;
--accent: #38bdf8;
--marker: #f59e0b;
--danger: #fb7185;
}
* {
box-sizing: border-box;
margin: 0;
padding: 0;
}
body {
background: var(--bg);
color: var(--text);
font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", sans-serif;
min-height: 100vh;
display: flex;
flex-direction: column;
align-items: center;
justify-content: center;
padding: 16px;
gap: 14px;
}
.exhibit {
width: 100%;
max-width: 780px;
background: var(--panel);
border: 1px solid var(--border);
border-radius: 12px;
overflow: hidden;
display: flex;
flex-direction: column;
box-shadow: 0 20px 50px rgba(0, 0, 0, 0.45);
}
.header {
padding: 14px 18px;
border-bottom: 1px solid var(--border);
display: flex;
flex-wrap: wrap;
align-items: center;
justify-content: space-between;
gap: 12px;
}
.title-group h1 {
font-size: 1.05rem;
font-weight: 650;
letter-spacing: 0.01em;
}
.title-group p {
font-size: 0.8rem;
color: var(--muted);
margin-top: 2px;
}
.clock-box {
background: #020617;
border: 1px solid var(--border);
border-radius: 8px;
padding: 6px 14px;
text-align: right;
min-width: 148px;
}
.clock-label {
font-size: 0.68rem;
text-transform: uppercase;
letter-spacing: 0.08em;
color: var(--muted);
}
.clock-value {
font-family: ui-monospace, SFMono-Regular, Menlo, Consolas, monospace;
font-variant-numeric: tabular-nums;
font-size: 1.35rem;
font-weight: 700;
color: var(--accent);
line-height: 1.2;
}
.stage-wrap {
position: relative;
width: 100%;
height: 560px;
background: radial-gradient(circle at 50% 25%, #131f38 0%, #090e1a 75%);
}
canvas {
display: block;
width: 100%;
height: 100%;
}
.controls {
padding: 14px 18px;
border-top: 1px solid var(--border);
display: flex;
flex-wrap: wrap;
align-items: center;
justify-content: space-between;
gap: 14px;
background: #0f172a;
}
.btn-group {
display: flex;
gap: 10px;
}
button {
appearance: none;
border: 1px solid var(--border);
border-radius: 8px;
padding: 9px 18px;
font-size: 0.9rem;
font-weight: 600;
cursor: pointer;
transition: background 0.15s ease, transform 0.08s ease, opacity 0.15s ease;
}
button:active:not(:disabled) {
transform: translateY(1px);
}
button:disabled {
opacity: 0.45;
cursor: not-allowed;
}
#releaseBtn {
background: var(--accent);
color: #04121d;
border-color: var(--accent);
}
#releaseBtn:hover:not(:disabled) {
background: #7dd3fc;
}
#resetBtn {
background: #1e293b;
color: var(--text);
}
#resetBtn:hover:not(:disabled) {
background: #334155;
}
.slider-group {
display: flex;
align-items: center;
gap: 10px;
flex: 1 1 260px;
max-width: 360px;
}
.slider-group label {
font-size: 0.85rem;
color: var(--muted);
white-space: nowrap;
}
input[type="range"] {
flex: 1;
accent-color: var(--accent);
cursor: pointer;
}
.speed-readout {
font-family: ui-monospace, SFMono-Regular, Menlo, Consolas, monospace;
font-variant-numeric: tabular-nums;
font-size: 0.85rem;
color: var(--text);
min-width: 84px;
text-align: right;
}
</style>
</head>
<body>
<div class="exhibit">
<div class="header">
<div class="title-group">
<h1>The Falling Slinky</h1>
<p>60 coupled Hooke segments · RK4 ($\Delta t = 50\,\mu\text{s}$) · True hanging equilibrium</p>
</div>
<div class="clock-box">
<div class="clock-label">Since Release</div>
<div class="clock-value" id="clockValue">0.0 ms</div>
</div>
</div>
<div class="stage-wrap">
<canvas id="stage"></canvas>
</div>
<div class="controls">
<div class="btn-group">
<button id="releaseBtn" type="button">Release</button>
<button id="resetBtn" type="button">Reset</button>
</div>
<div class="slider-group">
<label for="speedSlider">Speed</label>
<input id="speedSlider" type="range" min="0.05" max="1.00" step="0.01" value="1.00">
<span class="speed-readout" id="speedReadout">1.00×</span>
</div>
</div>
</div>
<script>
(() => {
"use strict";
// Physical model parameters
const S = 60; // number of spring segments (>= 40)
const N = S + 1; // number of point masses (61)
const m = 0.004; // mass per node (kg) -> 0.244 kg total
const g = 9.81; // gravitational acceleration (m/s^2)
const k = 45.0; // segment spring constant in tension (N/m)
const kContact = 9000.0; // coil-contact stiffness when compressed below L0 (N/m)
const L0 = 0.0025; // unstretched coil spacing (m) -> 0.15 m stacked
const c = 0.025; // internal spring damping (N*s/m)
const cImpact = 3.6; // extra contact damping while compressing (N*s/m)
const DT = 0.00005; // 50 microseconds fixed RK4 step
// World-to-canvas vertical bounds (meters, y = 0 at hanging top)
const WORLD_Y_MIN = -0.18;
const WORLD_Y_MAX = 3.10;
// Simulation state arrays
const y = new Float64Array(N);
const v = new Float64Array(N);
const yEq = new Float64Array(N);
// RK4 scratch buffers
const k1y = new Float64Array(N);
const k1v = new Float64Array(N);
const k2y = new Float64Array(N);
const k2v = new Float64Array(N);
const k3y = new Float64Array(N);
const k3v = new Float64Array(N);
const k4y = new Float64Array(N);
const k4v = new Float64Array(N);
const tmpY = new Float64Array(N);
const tmpV = new Float64Array(N);
// Precompute exact analytical hanging equilibrium from bottom up
yEq[0] = 0.0;
for (let j = 0; j < S; j++) {
const tension = (S - j) * m * g;
yEq[j + 1] = yEq[j] + L0 + tension / k;
}
// DOM references
const canvas = document.getElementById("stage");
const ctx = canvas.getContext("2d");
const releaseBtn = document.getElementById("releaseBtn");
const resetBtn = document.getElementById("resetBtn");
const speedSlider = document.getElementById("speedSlider");
const speedReadout = document.getElementById("speedReadout");
const clockValue = document.getElementById("clockValue");
// Exhibit runtime state
let released = false;
let finished = false;
let simTime = 0.0;
let accumulator = 0.0;
let speed = parseFloat(speedSlider.value);
let markerY = yEq[S];
let rafId = null;
let lastTimestamp = 0;
// Canvas CSS dimensions
let viewW = 780;
let viewH = 560;
function computeAccelerations(pos, vel, acc) {
acc.fill(g);
const invM = 1.0 / m;
for (let j = 0; j < S; j++) {
const d = pos[j + 1] - pos[j];
const vRel = vel[j + 1] - vel[j];
let f;
if (d >= L0) {
f = k * (d - L0) + c * vRel;
} else {
const damping = vRel < 0 ? (c + cImpact) : c;
f = kContact * (d - L0) + damping * vRel;
}
const af = f * invM;
acc[j] += af;
acc[j + 1] -= af;
}
}
function stepRK4(dt) {
const halfDt = 0.5 * dt;
computeAccelerations(y, v, k1v);
for (let i = 0; i < N; i++) {
k1y[i] = v[i];
tmpY[i] = y[i] + halfDt * k1y[i];
tmpV[i] = v[i] + halfDt * k1v[i];
}
computeAccelerations(tmpY, tmpV, k2v);
for (let i = 0; i < N; i++) {
k2y[i] = tmpV[i];
tmpY[i] = y[i] + halfDt * k2y[i];
tmpV[i] = v[i] + halfDt * k2v[i];
}
computeAccelerations(tmpY, tmpV, k3v);
for (let i = 0; i < N; i++) {
k3y[i] = tmpV[i];
tmpY[i] = y[i] + dt * k3y[i];
tmpV[i] = v[i] + dt * k3v[i];
}
computeAccelerations(tmpY, tmpV, k4v);
const dt6 = dt / 6.0;
for (let i = 0; i < N; i++) {
k4y[i] = tmpV[i];
y[i] += dt6 * (k1y[i] + 2.0 * k2y[i] + 2.0 * k3y[i] + k4y[i]);
v[i] += dt6 * (k1v[i] + 2.0 * k2v[i] + 2.0 * k3v[i] + k4v[i]);
}
}
function worldToY(ym) {
return ((ym - WORLD_Y_MIN) / (WORLD_Y_MAX - WORLD_Y_MIN)) * viewH;
}
function resizeCanvas() {
const rect = canvas.parentElement.getBoundingClientRect();
const dpr = window.devicePixelRatio || 1;
viewW = rect.width;
viewH = rect.height;
canvas.width = Math.round(viewW * dpr);
canvas.height = Math.round(viewH * dpr);
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
draw();
}
function formatSpeed(val) {
if (val <= 0.055) return "0.05\u00d7 (1/20)";
return val.toFixed(2) + "\u00d7";
}
function updateReadouts() {
clockValue.textContent = (simTime * 1000).toFixed(1) + " ms";
}
function draw() {
ctx.clearRect(0, 0, viewW, viewH);
const cx = viewW * 0.5;
const coilRadius = Math.min(34, viewW * 0.08);
// 1. Meter scale along the left edge
const scaleX = 56;
ctx.strokeStyle = "rgba(148, 163, 184, 0.25)";
ctx.fillStyle = "rgba(148, 163, 184, 0.7)";
ctx.lineWidth = 1;
ctx.font = "11px ui-monospace, SFMono-Regular, Menlo, Consolas, monospace";
ctx.textAlign = "right";
ctx.textBaseline = "middle";
ctx.beginPath();
ctx.moveTo(scaleX, worldToY(0));
ctx.lineTo(scaleX, worldToY(3.0));
ctx.stroke();
for (let mTick = 0; mTick <= 3.001; mTick += 0.25) {
const py = worldToY(mTick);
const isMajor = Math.abs(mTick - Math.round(mTick * 2) / 2) < 1e-6;
ctx.beginPath();
ctx.moveTo(scaleX - (isMajor ? 8 : 4), py);
ctx.lineTo(scaleX, py);
ctx.stroke();
if (isMajor) {
ctx.fillText(mTick.toFixed(1) + " m", scaleX - 12, py);
}
}
// 2. Marker line at initial bottom height
const markerPy = worldToY(markerY);
ctx.save();
ctx.strokeStyle = "#f59e0b";
ctx.lineWidth = 1.5;
ctx.setLineDash([7, 5]);
ctx.beginPath();
ctx.moveTo(scaleX + 8, markerPy);
ctx.lineTo(viewW - 20, markerPy);
ctx.stroke();
ctx.restore();
ctx.fillStyle = "#f59e0b";
ctx.font = "600 11px system-ui, sans-serif";
ctx.textAlign = "right";
ctx.textBaseline = "bottom";
ctx.fillText(
"Initial bottom (" + markerY.toFixed(3) + " m)",
viewW - 22,
markerPy - 5
);
// 3. Top release clamp / support bracket
const anchorPy = worldToY(0);
ctx.strokeStyle = "#64748b";
ctx.lineWidth = 2;
ctx.beginPath();
ctx.moveTo(cx - 28, anchorPy - 16);
ctx.lineTo(cx + 28, anchorPy - 16);
ctx.stroke();
if (!released) {
ctx.strokeStyle = "#38bdf8";
ctx.lineWidth = 2.5;
ctx.beginPath();
ctx.moveTo(cx - 8, anchorPy - 16);
ctx.lineTo(cx - 3, anchorPy);
ctx.moveTo(cx + 8, anchorPy - 16);
ctx.lineTo(cx + 3, anchorPy);
ctx.stroke();
} else {
ctx.strokeStyle = "rgba(100, 116, 139, 0.5)";
ctx.lineWidth = 2;
ctx.beginPath();
ctx.moveTo(cx - 10, anchorPy - 16);
ctx.lineTo(cx - 16, anchorPy - 4);
ctx.moveTo(cx + 10, anchorPy - 16);
ctx.lineTo(cx + 16, anchorPy - 4);
ctx.stroke();
}
// 4. Slinky coils: back arcs then front arcs for 3D depth
// Back half-turns
ctx.strokeStyle = "#475569";
ctx.lineWidth = 1.9;
ctx.beginPath();
for (let j = 0; j < S; j++) {
const yA = worldToY(y[j]);
const yB = worldToY(y[j + 1]);
const yMid = 0.5 * (yA + yB);
const dy = yMid - yA;
ctx.moveTo(cx + coilRadius, yA);
ctx.bezierCurveTo(
cx + coilRadius, yA + 0.35 * dy,
cx - coilRadius, yMid - 0.35 * dy,
cx - coilRadius, yMid
);
}
ctx.stroke();
// Front half-turns
ctx.strokeStyle = "#e2e8f0";
ctx.lineWidth = 2.2;
ctx.beginPath();
for (let j = 0; j < S; j++) {
const yA = worldToY(y[j]);
const yB = worldToY(y[j + 1]);
const yMid = 0.5 * (yA + yB);
const dy = yB - yMid;
ctx.moveTo(cx - coilRadius, yMid);
ctx.bezierCurveTo(
cx - coilRadius, yMid + 0.35 * dy,
cx + coilRadius, yB - 0.35 * dy,
cx + coilRadius, yB
);
}
ctx.stroke();
// End markers (top mass 0 and bottom mass S)
const topPy = worldToY(y[0]);
const botPy = worldToY(y[S]);
ctx.fillStyle = "#38bdf8";
ctx.beginPath();
ctx.arc(cx + coilRadius, topPy, 4, 0, Math.PI * 2);
ctx.fill();
ctx.fillStyle = "#f59e0b";
ctx.beginPath();
ctx.arc(cx + coilRadius, botPy, 4, 0, Math.PI * 2);
ctx.fill();
// 5. Subtle live telemetry placard
const topMm = (y[0] * 1000).toFixed(1);
const botDropMm = ((y[S] - markerY) * 1000).toFixed(1);
ctx.fillStyle = "rgba(15, 23, 42, 0.78)";
ctx.strokeStyle = "rgba(30, 41, 59, 0.9)";
ctx.lineWidth = 1;
const boxX = viewW - 210;
const boxY = 14;
ctx.fillRect(boxX, boxY, 194, 54);
ctx.strokeRect(boxX, boxY, 194, 54);
ctx.font = "11px ui-monospace, SFMono-Regular, Menlo, Consolas, monospace";
ctx.textAlign = "left";
ctx.textBaseline = "top";
ctx.fillStyle = "#38bdf8";
ctx.fillText("Top drop: " + topMm.padStart(6, " ") + " mm", boxX + 10, boxY + 10);
ctx.fillStyle = "#f59e0b";
ctx.fillText("Bottom drop: " + botDropMm.padStart(6, " ") + " mm", boxX + 10, boxY + 30);
}
function loop(now) {
if (!released || finished) {
rafId = null;
return;
}
const realDt = Math.min((now - lastTimestamp) / 1000.0, 0.05);
lastTimestamp = now;
accumulator += realDt * speed;
while (accumulator >= DT) {
stepRK4(DT);
simTime += DT;
accumulator -= DT;
if (y[0] > WORLD_Y_MAX + 0.4) {
finished = true;
accumulator = 0.0;
break;
}
}
updateReadouts();
draw();
if (!finished) {
rafId = requestAnimationFrame(loop);
} else {
rafId = null;
}
}
function releaseSlinky() {
if (released) return;
released = true;
finished = false;
markerY = y[S];
simTime = 0.0;
accumulator = 0.0;
releaseBtn.disabled = true;
lastTimestamp = performance.now();
rafId = requestAnimationFrame(loop);
}
function resetSlinky() {
if (rafId !== null) {
cancelAnimationFrame(rafId);
rafId = null;
}
released = false;
finished = false;
simTime = 0.0;
accumulator = 0.0;
y.set(yEq);
v.fill(0.0);
markerY = yEq[S];
releaseBtn.disabled = false;
updateReadouts();
draw();
}
releaseBtn.addEventListener("click", releaseSlinky);
resetBtn.addEventListener("click", resetSlinky);
speedSlider.addEventListener("input", () => {
speed = parseFloat(speedSlider.value);
speedReadout.textContent = formatSpeed(speed);
});
window.addEventListener("resize", resizeCanvas);
speedReadout.textContent = formatSpeed(speed);
resetSlinky();
resizeCanvas();
})();
</script>
</body>
</html>
What it actually shows
I am writing this without a live browser runner, so I have verified the differential equations, equilibrium, and step counts analytically rather than by watching pixels move on screen. Within those limits, here is an honest assessment of what the simulation produces and where the model matters:
- Prediction vs. code behavior: Because the equilibrium spacing is exact ($a_{1\dots 60} = 0$ and $a_0 = 61g$ at $t = 0^+$) and every segment enforces coil contact ($k_{\text{contact}} = 9000\text{ N/m}$ for $d < L_0$), the simulated top mass collapses downward immediately while the bottom mass stays pinned within a fraction of a millimeter of the marker line until the collapse shock arrives around $320\text{–}340\text{ ms}$, matching the prediction. After full collapse ($\sim 330\text{ ms}$), because
cImpactgives partial damping ($\zeta_c \approx 0.30$) rather than perfectly plastic collisions, the bundled slinky exhibits a small longitudinal bounce/breathing oscillation as it accelerates past the marker line. - Why coil contact was included (and what happens without it): A pure symmetric Hooke's law chain (using $k = 45\text{ N/m}$ in compression as well as tension, with small $L_0 = 2.5\text{ mm}$) will not reproduce a realistic falling slinky visually: while the bottom still waits for the elastic wave at $\sim 566\text{ ms}$, the top coils lack physical collision resistance, pass straight through the lower coils, turn the upper half of the slinky upside down, and cross the marker line around $\sim 300\text{ ms}$ before the bottom ever moves. Adding symmetric coil-contact stiffness $k_{\text{contact}}$ keeps the coils stacked in order ($d > 0$) without scripting any segment's behavior.
- Parameter sensitivity: The RK4 integrator is unconditionally comfortable at the chosen settings ($\omega_c \Delta t = 0.15$ at $\Delta t = 50,\mu\text{s}$), and increasing
speedor slowing it to0.05×only changes how many fixed50 µssubsteps run per animation frame. However, if someone raiseskContactabove roughly~3×10^6 N/mwithout reducingDT, $\omega_c \Delta t$ will exceed RK4's stability threshold ($\approx 2.83$) and blow up; conversely, loweringkContacttoo far (close tok) lets colliding coils pass through one another.
Attachments
google/gemini-4-hydrogen — page