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math

E=mc2E = mc^2
Mass–energy equivalence

code

oscillator.ts
const damping = 0.25;
const frequency = 2;
const duration = 10;
const samples = 300;

const omegaD = frequency * Math.sqrt(1 - damping ** 2);
const displacement = (t: number) =>
  Math.exp(-damping * frequency * t) * Math.cos(omegaD * t);

const points = Array.from({ length: samples }, (_, i) => {
  const time = (i / (samples - 1)) * duration;
  return { time, value: displacement(time) };
});

chart

Synthetic data

A damped oscillator

Synthetic data with damping ratio 0.12.

Original CSV Shift + scroll to zoom · drag to pan
Data and export

Inspect the prepared rows plotted in this chart, or save the current chart view.

The table loads alongside the chart.

Page 1 of 1

model

A torus knot

Drag to inspect this generated teaching mesh.

Static view of A torus knot

Drag to orbit · Shift + scroll to zoom

View options
Download model

shader

Two wave sources

audio

Three tones

Settings

A synthetic 30-second listening study.

Download audio
Transcript

0:00 — A quiet 220 Hz tone. 0:10 — The tone rises to 330 Hz. 0:20 — The tone rises to 440 Hz, then fades out.

video

Wave study

Settings

Synthetic motion and tones, with two caption languages and three chapters.

Download video
Transcript

0:00 — Blue waves drift across the frame over a low tone. 0:10 — The tone rises as the wave pattern continues. 0:20 — The final higher tone fades out with the study.

midi

⋯

Draw to add · drag to move · drag edge to resize

Editor loads when visible.
Warm keys: C4Warm keys: E4Warm keys: G4Warm keys: C5Warm keys: B3Warm keys: D4Warm keys: G4Warm keys: B4Warm keys: A3Warm keys: C4Warm keys: E4Warm keys: A4Warm keys: G3Warm keys: B3Warm keys: D4Warm keys: G4Warm keys: C4Warm keys: E4Warm keys: G4Warm keys: B4Warm keys: A3Warm keys: C4Warm keys: E4Warm keys: A4Warm keys: G3Warm keys: B3Warm keys: D4Warm keys: G4Warm keys: F3Warm keys: A3Warm keys: C4Warm keys: F4
Accessible note list
  • Warm keys: C4, beat 0, for 3.44 beats
  • Warm keys: E4, beat 0, for 3.44 beats
  • Warm keys: G4, beat 0, for 3.44 beats
  • Warm keys: C5, beat 0, for 3.44 beats
  • Warm keys: B3, beat 4, for 3.44 beats
  • Warm keys: D4, beat 4, for 3.44 beats
  • Warm keys: G4, beat 4, for 3.44 beats
  • Warm keys: B4, beat 4, for 3.44 beats
  • Warm keys: A3, beat 8, for 3.44 beats
  • Warm keys: C4, beat 8, for 3.44 beats
  • Warm keys: E4, beat 8, for 3.44 beats
  • Warm keys: A4, beat 8, for 3.44 beats
  • Warm keys: G3, beat 12, for 3.44 beats
  • Warm keys: B3, beat 12, for 3.44 beats
  • Warm keys: D4, beat 12, for 3.44 beats
  • Warm keys: G4, beat 12, for 3.44 beats
  • Warm keys: C4, beat 16, for 3.44 beats
  • Warm keys: E4, beat 16, for 3.44 beats
  • Warm keys: G4, beat 16, for 3.44 beats
  • Warm keys: B4, beat 16, for 3.44 beats
  • Warm keys: A3, beat 20, for 3.44 beats
  • Warm keys: C4, beat 20, for 3.44 beats
  • Warm keys: E4, beat 20, for 3.44 beats
  • Warm keys: A4, beat 20, for 3.44 beats
  • Warm keys: G3, beat 24, for 3.44 beats
  • Warm keys: B3, beat 24, for 3.44 beats
  • Warm keys: D4, beat 24, for 3.44 beats
  • Warm keys: G4, beat 24, for 3.44 beats
  • Warm keys: F3, beat 28, for 3.44 beats
  • Warm keys: A3, beat 28, for 3.44 beats
  • Warm keys: C4, beat 28, for 3.44 beats
  • Warm keys: F4, beat 28, for 3.44 beats

Edit a phrase, compare the voices, and export the result.

post-list

table-of-contents

Introduction

This content gives the navigation a real destination.

First example

Heading depth determines indentation.

Reference

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