Run Detail
completedparticle-1Recorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
71.5s
Total Tokens
25,696
Input Tokens
821
Output Tokens
24,875
Reasoning Tokens
21,754
Reasoning Effort
default
Est. Cost
$0.0251
Started
10/28/2026, 8:15:21 PM
OR Provider
Particle AI
Finish Reason
stop
Generation ID
gen-1793218519-3EfgRmyKbznJJr5mKvEN
Turns (1)
Turn #1
821 in24,875 out21,754 reasoning25,696 total71.5s
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
When the top is released, the top segment is no longer held up, so it accelerates downward at roughly (N g) (about (50g) for 50 segments) because the stretched spring below it pulls it down in addition to gravity. This creates a compression front that travels down the slinky. The bottom segment, however, initially feels exactly the same forces as before release: gravity downward balanced by the tension from the coil above it. Until the compression front reaches it, it has no reason to move. So the bottom stays almost exactly at its release height for roughly the wave-travel time — about 0.3 s for these parameters — while the top collapses downward. After the front arrives, the bottom begins to fall, and the whole slinky is in free fall (with internal oscillations). At 1/20 speed, the bottom should appear frozen against the marker line for several seconds before dropping.
The setup
- Segments: (N = 50).
- Mass per segment: (m = 1.0).
- Gravity: (g = 9.8).
- Spring constant: (k = 28000) N/m per segment.
- Natural length: (L_0 = 0.001) m.
- Damping: (c = 5.0) N·s/m between neighbours.
- Timestep: (\Delta t = 0.0001) s.
- Integrator: velocity Verlet (symplectic, second-order).
The hanging equilibrium is solved analytically. The tension in the spring between segment (i) and (i+1) must support the weight of everything below it, so (T_i = (N-1-i)mg). The equilibrium spacing is therefore (L_0 + T_i/k). Starting from the top at (y=0), the positions are accumulated downward. This gives the exact static equilibrium, so the slinky is genuinely at rest before release. The top segment is pinned only while hanging; after release every segment obeys the same force law.
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>
html, body {
margin: 0; padding: 0; height: 100%; overflow: hidden;
background: #0d1117; color: #e6edf3;
font-family: system-ui, -apple-system, sans-serif;
}
#canvas { display: block; width: 100%; height: 100%; }
#ui {
position: absolute; top: 16px; left: 16px;
background: rgba(13, 17, 23, 0.85);
border: 1px solid #30363d;
padding: 14px 16px; border-radius: 10px;
font-size: 14px; user-select: none;
backdrop-filter: blur(4px);
}
#ui button {
margin-right: 8px; padding: 7px 14px;
font-size: 14px; cursor: pointer;
background: #21262d; color: #e6edf3;
border: 1px solid #30363d; border-radius: 6px;
}
#ui button:hover { background: #30363d; }
#ui button:active { background: #161b22; }
#ui label { display: block; margin-top: 10px; }
#ui input[type=range] { width: 160px; vertical-align: middle; }
#clock {
font-variant-numeric: tabular-nums;
font-size: 20px; margin-top: 10px;
color: #58a6ff; font-weight: 600;
}
.hint { font-size: 11px; color: #8b949e; margin-top: 6px; }
</style>
</head>
<body>
<canvas id="canvas"></canvas>
<div id="ui">
<button id="release">Release</button>
<button id="reset">Reset</button>
<label>Speed: <input id="speed" type="range" min="0.05" max="1" step="0.01" value="1"> <span id="speedVal">1.00×</span></label>
<div id="clock">0 ms</div>
<div class="hint">Yellow line = bottom at release</div>
</div>
<script>
(function(){
'use strict';
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// ---- Physics parameters ----
const N = 50;
const m = 1.0;
const g = 9.8;
const k = 28000;
const L0 = 0.001;
const cDamp = 5.0;
const dt = 0.0001;
// ---- State ----
const y = new Float64Array(N);
const v = new Float64Array(N);
const F = new Float64Array(N);
const vHalf = new Float64Array(N);
let released = false;
let simTime = 0;
let markerY = null;
let speed = 1.0;
let lastRealTime = null;
let accumulator = 0;
// ---- Equilibrium positions ----
const yEq = new Float64Array(N);
yEq[0] = 0;
for (let i = 0; i < N - 1; i++) {
yEq[i + 1] = yEq[i] + L0 + (N - 1 - i) * m * g / k;
}
const totalLength = yEq[N - 1];
// ---- Reset ----
function reset() {
for (let i = 0; i < N; i++) {
y[i] = yEq[i];
v[i] = 0;
}
released = false;
simTime = 0;
markerY = null;
accumulator = 0;
lastRealTime = null;
document.getElementById('clock').textContent = '0 ms';
}
// ---- Forces ----
function computeForces(yArr, vArr, fArr) {
for (let i = 0; i < N; i++) {
let f = m * g;
if (i < N - 1) {
f += k * (yArr[i + 1] - yArr[i] - L0) + cDamp * (vArr[i + 1] - vArr[i]);
}
if (i > 0) {
f -= k * (yArr[i] - yArr[i - 1] - L0) + cDamp * (vArr[i] - vArr[i - 1]);
}
fArr[i] = f;
}
}
// ---- Velocity Verlet step ----
function step() {
computeForces(y, v, F);
for (let i = 0; i < N; i++) {
vHalf[i] = v[i] + 0.5 * dt * F[i] / m;
y[i] += dt * vHalf[i];
}
computeForces(y, vHalf, F);
for (let i = 0; i < N; i++) {
v[i] = vHalf[i] + 0.5 * dt * F[i] / m;
}
if (!released) {
y[0] = 0;
v[0] = 0;
}
simTime += dt;
}
// ---- Rendering ----
let scale = 1;
let offsetX = 0;
let offsetY = 0;
function resize() {
const dpr = window.devicePixelRatio || 1;
const W = window.innerWidth;
const H = window.innerHeight;
canvas.width = W * dpr;
canvas.height = H * dpr;
canvas.style.width = W + 'px';
canvas.style.height = H + 'px';
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
scale = 0.65 * H / totalLength;
offsetX = W / 2;
offsetY = 0.12 * H;
}
window.addEventListener('resize', resize);
function draw() {
const W = window.innerWidth;
const H = window.innerHeight;
ctx.clearRect(0, 0, W, H);
ctx.fillStyle = '#0d1117';
ctx.fillRect(0, 0, W, H);
// Marker line
if (markerY !== null) {
const py = offsetY + markerY * scale;
ctx.strokeStyle = 'rgba(255, 200, 0, 0.75)';
ctx.lineWidth = 1.5;
ctx.setLineDash([7, 7]);
ctx.beginPath();
ctx.moveTo(0, py);
ctx.lineTo(W, py);
ctx.stroke();
ctx.setLineDash([]);
ctx.fillStyle = 'rgba(255, 200, 0, 0.9)';
ctx.font = '12px system-ui, sans-serif';
ctx.fillText('bottom at release', 12, py - 7);
}
// Anchor
const ax = offsetX;
const ay = offsetY;
ctx.fillStyle = '#8b949e';
ctx.beginPath();
ctx.arc(ax, ay, 5, 0, Math.PI * 2);
ctx.fill();
ctx.strokeStyle = '#30363d';
ctx.lineWidth = 1;
ctx.beginPath();
ctx.arc(ax, ay, 8, 0, Math.PI * 2);
ctx.stroke();
// Screen points with zigzag
const pts = [];
for (let i = 0; i < N; i++) {
const px = offsetX + 9 * Math.sin(i * 1.25);
const py = offsetY + y[i] * scale;
pts.push([px, py]);
}
// Connecting line
ctx.strokeStyle = '#58a6ff';
ctx.lineWidth = 2.2;
ctx.lineJoin = 'round';
ctx.beginPath();
ctx.moveTo(pts[0][0], pts[0][1]);
for (let i = 1; i < N; i++) {
ctx.lineTo(pts[i][0], pts[i][1]);
}
ctx.stroke();
// Segment dots
for (let i = 0; i < N; i++) {
ctx.fillStyle = i === 0 ? '#ffffff' : '#58a6ff';
ctx.beginPath();
ctx.arc(pts[i][0], pts[i][1], i === 0 ? 4 : 2.8, 0, Math.PI * 2);
ctx.fill();
}
// Bottom highlight
const bx = pts[N - 1][0];
const by = pts[N - 1][1];
ctx.strokeStyle = '#f85149';
ctx.lineWidth = 2;
ctx.beginPath();
ctx.arc(bx, by, 6, 0, Math.PI * 2);
ctx.stroke();
}
// ---- Animation loop ----
function animate(now) {
if (lastRealTime === null) lastRealTime = now;
let realDt = (now - lastRealTime) / 1000;
lastRealTime = now;
if (realDt > 0.1) realDt = 0.1;
if (released) {
accumulator += realDt * speed;
let steps = 0;
while (accumulator >= dt && steps < 10000) {
step();
accumulator -= dt;
steps++;
}
document.getElementById('clock').textContent = Math.round(simTime * 1000) + ' ms';
}
draw();
requestAnimationFrame(animate);
}
// ---- Controls ----
document.getElementById('release').addEventListener('click', function() {
if (!released) {
released = true;
markerY = y[N - 1];
lastRealTime = null;
accumulator = 0;
}
});
document.getElementById('reset').addEventListener('click', function() {
reset();
});
const speedSlider = document.getElementById('speed');
const speedVal = document.getElementById('speedVal');
speedSlider.addEventListener('input', function() {
speed = parseFloat(speedSlider.value);
speedVal.textContent = speed.toFixed(2) + '×';
});
// ---- Init ----
resize();
reset();
requestAnimationFrame(animate);
})();
</script>
</body>
</html>
What it actually shows
I have not run this in a browser, so I cannot claim to have watched it. Based on the physics and the chosen parameters, I expect it to reproduce the prediction: the bottom segment should stay within a few pixels of the yellow marker line for roughly 0.3 s of simulated time (about 6 s at 1/20 speed), while the top collapses downward at an initial acceleration near (50g). After the compression front reaches the bottom, the whole slinky falls and oscillates.
The main uncertainty is the discrete wave front: with only 50 segments and finite damping, the bottom may creep slightly before the main collapse arrives, and the top may show visible high-frequency jitter. If the jitter is too distracting, increasing cDamp (e.g. to 15–20) will smooth it without changing the qualitative result. If the bottom drifts too early, the likely cause is numerical dispersion at the wave front; reducing dt further (e.g. to (5\times10^{-5})) would sharpen it. The parameters above are my best estimate for a stable, visually clear demonstration, but I would verify the marker-line behaviour before putting it in front of a physicist.
Attachments
particle-ai/particle-1 — page