Run Detail
completedgrok-4.6Recorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
199.1s
Total Tokens
13,588
Input Tokens
935
Output Tokens
12,653
Reasoning Tokens
9,374
Reasoning Effort
default
Cached Input Tokens
128
Est. Cost
$0.0776
Started
8/15/2026, 1:47:31 AM
OR Provider
xAI
Finish Reason
stop
Generation ID
gen-1786758452-dSP03mCbRBCKmbPfpHHk
Turns (1)
Turn #1
935 in12,653 out9,374 reasoning128 cached13,588 total199.1s
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 few hundred milliseconds after release the top end will drop at once — and faster than free-fall, because it loses the upward support of the mount while the still-stretched spring beneath it is still pulling downward. The bottom end will stay put on the marker line, to the eye motionless. A rarefaction/collapse travels down the coil: each mass remains in equilibrium under gravity and its two Hooke forces until the neighbour above it moves and unloads the spring. Only when that wave reaches the last mass — around 400–700 ms with the parameters below — does the bottom leave the marker, after which the bunched slinky falls as one. That delay is required: release changes the force on the top mass alone, and the rest of the chain cannot know until elasticity carries the news.
The setup
- Segments: 50 point masses, 49 identical springs (top mass is held fixed until Release; after Release every mass obeys the same force law and the same integrator — nothing pinned, delayed, or special-cased).
- Mass (m = 1), spring constant (k = 2200), rest length (L_0 = 2.5) (pixels), gravity (g = 700) (pixels/s², +y down), damping (c = 4) on relative velocity of each neighbouring pair (linear dashpot, not a velocity clamp).
- Timestep (\Delta t = 2\times 10^{-4}) s. Highest single-spring frequency (\sqrt{k/m}\approx 47) rad/s, so (\Delta t,\omega \approx 0.009).
- Integrator: semi-implicit Euler, many substeps per frame. No position/velocity clamps.
- Hanging equilibrium: closed form, not a relaxation. Spring (i) (between masses (i) and (i+1)) supports exactly the weight of the (N-1-i) masses below it, so its extension is ((N-1-i),mg/k). Positions are the cumulative sum of (L_0) plus that extension, velocities zero. Force balance on every free mass is then identically zero, and the coil spacing is visibly larger at the top than at the bottom.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Falling Slinky</title>
<style>
* { box-sizing: border-box; margin: 0; padding: 0; }
html, body {
background: #1a1d23;
color: #e8e4dc;
font-family: Georgia, "Times New Roman", serif;
min-height: 100%;
}
body {
display: flex;
flex-direction: column;
align-items: center;
padding: 18px 16px 32px;
}
h1 {
font-weight: normal;
font-size: 28px;
letter-spacing: 0.04em;
margin-bottom: 6px;
}
.lede {
font-size: 15px;
color: #b7b1a6;
margin-bottom: 16px;
max-width: 480px;
text-align: center;
line-height: 1.4;
}
.panel {
display: flex;
flex-wrap: wrap;
gap: 12px 18px;
align-items: center;
justify-content: center;
background: #242830;
border: 1px solid #3a3f4a;
padding: 12px 16px;
margin-bottom: 14px;
width: 480px;
}
button {
font-family: system-ui, sans-serif;
font-size: 15px;
padding: 8px 16px;
border: 1px solid #6a6458;
background: #3d382f;
color: #f0ebe3;
cursor: pointer;
}
button:hover { background: #524c40; }
button:active { background: #2a261f; }
label {
font-family: system-ui, sans-serif;
font-size: 13px;
color: #c9c3b8;
display: flex;
align-items: center;
gap: 8px;
}
input[type="range"] { width: 140px; }
#clock {
font-family: ui-monospace, "Cascadia Code", "Courier New", monospace;
font-size: 22px;
min-width: 118px;
text-align: right;
color: #f3d27a;
letter-spacing: 0.04em;
}
canvas {
background: #12141a;
border: 1px solid #3a3f4a;
display: block;
}
.caption {
margin-top: 10px;
font-size: 13px;
color: #8e887c;
max-width: 480px;
text-align: center;
line-height: 1.35;
}
</style>
</head>
<body>
<h1>Falling Slinky</h1>
<p class="lede">Fifty masses, forty-nine springs, gravity, a little damping. Hang, then let go. Watch the bottom against the line.</p>
<div class="panel">
<button type="button" id="btnRelease">Release</button>
<button type="button" id="btnReset">Reset</button>
<label>Speed
<input type="range" id="spd" min="0.05" max="1" step="0.01" value="1">
<span id="spdLabel">1×</span>
</label>
<div id="clock">0 ms</div>
</div>
<canvas id="c" width="480" height="720"></canvas>
<p class="caption">Yellow line marks the bottom coil at the instant of release. It does not move.</p>
<script>
(function () {
const N = 50;
const MASS = 1;
const K = 2200;
const L0 = 2.5;
const G = 700;
const C = 4;
const DT = 0.0002;
const Y_HOLD = 48;
const VIEW_W = 480;
const VIEW_H = 720;
const y = new Float64Array(N);
const v = new Float64Array(N);
const F = new Float64Array(N);
let released = false;
let simTime = 0;
let markerY = 0;
let speed = 1;
const canvas = document.getElementById("c");
const ctx = canvas.getContext("2d");
const clockEl = document.getElementById("clock");
const spdEl = document.getElementById("spd");
const spdLabel = document.getElementById("spdLabel");
function fitCanvas() {
const dpr = window.devicePixelRatio || 1;
canvas.width = Math.round(VIEW_W * dpr);
canvas.height = Math.round(VIEW_H * dpr);
canvas.style.width = VIEW_W + "px";
canvas.style.height = VIEW_H + "px";
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
}
function hang() {
y[0] = Y_HOLD;
v[0] = 0;
for (let i = 1; i < N; i++) {
const massesSupported = N - i;
y[i] = y[i - 1] + L0 + (massesSupported * MASS * G) / K;
v[i] = 0;
}
markerY = y[N - 1];
released = false;
simTime = 0;
clockEl.textContent = "0 ms";
}
function accelerations() {
for (let i = 0; i < N; i++) F[i] = G;
for (let i = 0; i < N - 1; i++) {
const dy = y[i + 1] - y[i];
const fs = (K * (dy - L0)) / MASS;
const fd = (C * (v[i + 1] - v[i])) / MASS;
F[i] += fs + fd;
F[i + 1] -= fs + fd;
}
}
function step() {
accelerations();
const i0 = released ? 0 : 1;
for (let i = i0; i < N; i++) {
v[i] += F[i] * DT;
y[i] += v[i] * DT;
}
if (!released) {
y[0] = Y_HOLD;
v[0] = 0;
}
}
function draw() {
ctx.clearRect(0, 0, VIEW_W, VIEW_H);
const cx = VIEW_W * 0.5;
const coilR = 78;
ctx.save();
ctx.strokeStyle = "rgba(243, 210, 122, 0.85)";
ctx.setLineDash([7, 6]);
ctx.lineWidth = 1.5;
ctx.beginPath();
ctx.moveTo(16, markerY);
ctx.lineTo(VIEW_W - 16, markerY);
ctx.stroke();
ctx.setLineDash([]);
ctx.restore();
ctx.fillStyle = "#4a4338";
ctx.fillRect(cx - 90, 18, 180, 8);
ctx.fillStyle = "#6a6358";
ctx.fillRect(cx - 6, 18, 12, released ? 10 : Y_HOLD - 18);
if (!released) {
ctx.strokeStyle = "#c45c4a";
ctx.lineWidth = 3;
ctx.beginPath();
ctx.moveTo(cx - 14, Y_HOLD - 10);
ctx.lineTo(cx - 10, Y_HOLD + 2);
ctx.lineTo(cx + 10, Y_HOLD + 2);
ctx.lineTo(cx + 14, Y_HOLD - 10);
ctx.stroke();
}
for (let i = 0; i < N; i++) {
const t = i / (N - 1);
const r = Math.round(168 + 40 * t);
const gcol = Math.round(122 + 20 * (1 - t));
const b = Math.round(72 + 18 * t);
ctx.strokeStyle = "rgb(" + r + "," + gcol + "," + b + ")";
ctx.lineWidth = 1.7;
ctx.beginPath();
ctx.ellipse(cx, y[i], coilR, 4.2, 0, 0, Math.PI * 2);
ctx.stroke();
if (i < N - 1) {
const mid = 0.5 * (y[i] + y[i + 1]);
ctx.globalAlpha = 0.55;
ctx.beginPath();
ctx.ellipse(cx, mid, coilR * 0.97, 3.6, 0, 0, Math.PI * 2);
ctx.stroke();
ctx.globalAlpha = 1;
}
}
ctx.fillStyle = "rgba(243, 210, 122, 0.35)";
ctx.font = "12px system-ui, sans-serif";
ctx.fillText("release height of bottom", 20, markerY - 8);
}
hang();
fitCanvas();
draw();
document.getElementById("btnRelease").addEventListener("click", function () {
released = true;
});
document.getElementById("btnReset").addEventListener("click", function () {
hang();
draw();
});
spdEl.addEventListener("input", function () {
speed = parseFloat(spdEl.value);
if (speed >= 0.995) spdLabel.textContent = "1×";
else spdLabel.textContent = speed.toFixed(2) + "×";
});
let last = performance.now();
function frame(now) {
const realDt = Math.min(0.05, (now - last) / 1000);
last = now;
if (released) {
const acc = realDt * speed;
simTime += acc;
let steps = Math.floor(acc / DT);
if (steps > 2500) steps = 2500;
for (let s = 0; s < steps; s++) step();
clockEl.textContent = Math.floor(simTime * 1000) + " ms";
}
draw();
requestAnimationFrame(frame);
}
requestAnimationFrame(frame);
window.addEventListener("resize", function () {
fitCanvas();
draw();
});
})();
</script>
</body>
</html>
What it actually shows
I have not opened this page in a browser, so I cannot honestly say I watched the bottom sit on the line. What I can say is narrower. The hanging positions are the exact static solution of the same force law the integrator uses, so at the moment of release the net force on every mass except the top one is zero and every velocity is zero. The step function applies one force routine to every free mass; after Release that set is all 50 of them. The bottom mass therefore cannot accelerate until mass 48 has moved enough to change the last spring, which cannot happen until the unloading has walked down the chain. That is the predicted picture, built in rather than painted on. Whether the arrival is 400 ms or 800 ms, and whether residual ringing after the pile-up looks tidy, I have not measured — those depend on (k), (L_0) and (c), and I did not tune them against a run. If you press Release and the bottom creeps off the marker from (t = 0), that is a bug in this file, not a revision of the claim.
Attachments
x-ai/grok-4.6 — page