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Simple Harmonic Oscillator

Đối tượng: UniversityThể loại: Physics

Mô tả

A mass-spring system oscillates while three synchronized displays show: position x(t), velocity v(t), and phase-space (x vs v) — an ellipse. A ValueTracker drives all three simultaneously.

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Simple Harmonic Oscillator

Description

A mass-spring system oscillates while three synchronized displays show: position x(t), velocity v(t), and phase-space (x vs v) — an ellipse. A ValueTracker drives all three simultaneously.

Phases

# Phase Name Duration Description
1 Setup 1.5s Spring-mass, axes, and formulas appear
2 Full Oscillation 6s All three displays animate in sync for 2 cycles
3 Phase Space Ellipse 2s Ellipse completes, labeled
4 Energy Formula 1.5s E = ½kA² displayed

Layout

+--------------------------------------------------+
|  Simple Harmonic Oscillator                      |
|                                                  |
|  [Spring-mass]   [x(t) sine graph]               |
|     ⌇⌇⌇[M]        [v(t) cosine graph]           |
|                   [Phase space ellipse]          |
|                                                  |
|  x(t) = A cos(ωt + φ)     E = ½kA²              |
+--------------------------------------------------+

Area Descriptions

  • Left: physical spring-mass animation
  • Right top: x(t) graph
  • Right middle: v(t) graph
  • Right bottom: phase space (x vs v)

Assets & Dependencies

  • Fonts: LaTeX / sans-serif
  • Manim version: ManimCE 0.19.1

Notes

  • University level
  • Use ValueTracker for time parameter
  • Phase space should trace an ellipse