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.

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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

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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)

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Assets & Dependencies

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

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Notes

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