Run Detail
completedbeam-1.0-501b-a23bRecorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
65.4s
Total Tokens
17,276
Input Tokens
779
Output Tokens
16,497
Reasoning Tokens
14,575
Reasoning Effort
default
Est. Cost
$0.0167
Started
10/16/2026, 4:38:30 PM
OR Provider
Nebius
Finish Reason
stop
Generation ID
gen-1792168710-0T1tLySlnlygfBOh3Qil
Turns (1)
Turn #1
779 in16,497 out14,575 reasoning17,276 total65.4s
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 of the slinky will accelerate downward very rapidly — initially about (N g) for the top coil, because its spring is stretched by the weight of all the coils below it — so the upper part collapses and falls while the lower part has not yet received the disturbance. The bottom coil has zero initial acceleration (its spring was supporting only its own weight), so it should remain essentially on the marker line during that early period; the visible action is a contraction wave moving downward from the top, with a sharp boundary between the already-collapsed upper coils and the still-stretched lower coils.
The setup
- 60 point masses, 59 springs; mass (m=1), gravity (g=10), spring constant (k=200), rest length (l_0=4), damping coefficient (0.5).
- Integration: semi-implicit Euler with fixed step (h=0.0005,\text{s}); the speed slider scales simulated time per frame, not the step size.
- Hanging equilibrium is solved exactly before release: the top mass is held at the support, and the spacing between masses (j-1) and (j) is (l_0+(N-j)mg/k), so the top coils are stretched more than the bottom coils.
- On release, no mass remains pinned or special-cased; every mass uses the same force rule, with boundary masses simply having one neighbour instead of two.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Falling Slinky</title>
<style>
html,body{margin:0;padding:0;background:#10131a;color:#e8ecf4;font-family:system-ui,sans-serif;}
#app{display:flex;flex-direction:column;align-items:center;padding:12px;gap:10px;}
canvas{background:#181c24;border:1px solid #3a4252;border-radius:6px;}
.controls{display:flex;flex-wrap:wrap;gap:12px;align-items:center;justify-content:center;}
button{padding:6px 12px;border:1px solid #5a6478;background:#232a36;color:#e8ecf4;border-radius:4px;cursor:pointer;}
button:hover{background:#2d3646;}
label{display:flex;align-items:center;gap:6px;}
input[type=range]{width:160px;}
.readout{font-variant-numeric:tabular-nums;}
</style>
</head>
<body>
<div id="app">
<div class="controls">
<button id="releaseBtn">Release</button>
<button id="resetBtn">Reset</button>
<label>Speed <input id="speed" type="range" min="5" max="100" value="100" step="5"></label>
<span id="speedVal" class="readout">1.00×</span>
<span class="readout">Clock: <span id="clock">0.0</span> ms</span>
</div>
<canvas id="c" width="480" height="640"></canvas>
</div>
<script>
(() => {
const canvas = document.getElementById('c');
const ctx = canvas.getContext('2d');
const N = 60;
const m = 1;
const g = 10;
const k = 200;
const l0 = 4;
const damp = 0.5;
const H = 0.0005;
const topY = 80;
const cx = canvas.width / 2;
let y = new Array(N);
let v = new Array(N);
let released = false;
let clockMs = 0;
let accumulator = 0;
let lastTime = null;
let markerY = null;
function equilibrium() {
y[0] = 0;
const q = m * g / k;
for (let j = 1; j < N; j++) {
const spacing = l0 + (N - j) * q;
y[j] = y[j - 1] + spacing;
}
}
function resetState() {
equilibrium();
for (let i = 0; i < N; i++) v[i] = 0;
released = false;
clockMs = 0;
accumulator = 0;
markerY = null;
lastTime = performance.now();
}
function integrate(h) {
const a = new Array(N);
for (let i = 0; i < N; i++) {
let acc = g;
if (i > 0) {
const L = y[i] - y[i - 1];
acc += (-k * (L - l0)) / m;
}
if (i < N - 1) {
const L = y[i + 1] - y[i];
acc += (k * (L - l0)) / m;
}
acc += -(damp / m) * v[i];
a[i] = acc;
}
for (let i = 0; i < N; i++) v[i] += a[i] * h;
for (let i = 0; i < N; i++) y[i] += v[i] * h;
}
const releaseBtn = document.getElementById('releaseBtn');
const resetBtn = document.getElementById('resetBtn');
const speedSlider = document.getElementById('speed');
const speedVal = document.getElementById('speedVal');
const clockEl = document.getElementById('clock');
releaseBtn.addEventListener('click', () => {
if (released) return;
released = true;
markerY = topY + y[N - 1];
clockMs = 0;
accumulator = 0;
lastTime = performance.now();
});
resetBtn.addEventListener('click', () => {
resetState();
});
speedSlider.addEventListener('input', () => {
speedVal.textContent = (speedSlider.value / 100).toFixed(2) + '×';
});
function draw() {
ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.fillStyle = '#6b7280';
ctx.beginPath();
ctx.arc(cx, topY, 4, 0, Math.PI * 2);
ctx.fill();
if (markerY !== null) {
ctx.strokeStyle = 'rgba(250,204,21,0.9)';
ctx.lineWidth = 2;
ctx.beginPath();
ctx.moveTo(0, markerY);
ctx.lineTo(canvas.width, markerY);
ctx.stroke();
}
ctx.strokeStyle = '#7dd3fc';
ctx.lineWidth = 2;
ctx.beginPath();
ctx.moveTo(cx, topY + y[0]);
for (let i = 1; i < N; i++) ctx.lineTo(cx, topY + y[i]);
ctx.stroke();
ctx.fillStyle = '#f8fafc';
for (let i = 0; i < N; i++) {
ctx.beginPath();
ctx.arc(cx, topY + y[i], 2.2, 0, Math.PI * 2);
ctx.fill();
}
}
function loop(now) {
if (lastTime === null) lastTime = now;
let dt = (now - lastTime) / 1000;
lastTime = now;
if (dt > 0.1) dt = 0.1;
if (released) {
const speed = speedSlider.value / 100;
accumulator += dt * speed;
let steps = 0;
while (accumulator >= H && steps < 2000) {
integrate(H);
clockMs += H * 1000;
accumulator -= H;
steps++;
}
} else {
accumulator = 0;
}
clockEl.textContent = clockMs.toFixed(1);
draw();
requestAnimationFrame(loop);
}
resetState();
requestAnimationFrame(loop);
})();
</script>
</body>
</html>
What it actually shows
I have not executed the file in this environment, so this is an expectation from the construction rather than an observed run. The code is set up so that the top should fall immediately while the bottom remains on the marker for the first few hundred milliseconds, because the bottom coil has zero initial acceleration and the disturbance must propagate down the chain. I am not certain of the exact wave arrival time or how much numerical dispersion may make the bottom drift slightly before the main wave arrives; if the bottom leaves the marker immediately, that would indicate a problem in the discrete integration rather than the intended physics. At the chosen stiffness and step size it should remain stable; much larger stiffness or step sizes could make it unstable.
Attachments
reflection/beam-1.0-501b-a23b — page