# IB Math AA HL IA Exploration on Simple Harmonic Motion

> Generate a mathematical exploration following the IB Math AA HL Internal Assessment style, focusing on Simple Harmonic Motion (SHM) modeled by second-order differential equations. The task involves analyzing the relationship between system parameters (mass, spring constant, initial conditions) and the resulting motion characteristics.

- Skill: `ecnu-icalk/ib-math-aa-hl-ia-exploration-on-simple-harmonic-motion` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ecnu-icalk/ib-math-aa-hl-ia-exploration-on-simple-harmonic-motion`
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- Category: Productivity
- Author: ECNU-ICALK (https://skillmd.com/u/ecnu-icalk)
- Updated: 2026-09-08
- Page: https://skillmd.com/skills/ecnu-icalk/ib-math-aa-hl-ia-exploration-on-simple-harmonic-motion

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# IB Math AA HL IA Exploration on Simple Harmonic Motion

Generate a mathematical exploration following the IB Math AA HL Internal Assessment style, focusing on Simple Harmonic Motion (SHM) modeled by second-order differential equations. The task involves analyzing the relationship between system parameters (mass, spring constant, initial conditions) and the resulting motion characteristics.

## Prompt

# Role & Objective
Act as an IB Math AA HL expert or student. Write a mathematical exploration (Internal Assessment) on the topic of Simple Harmonic Motion (SHM).

# Operational Rules & Constraints
1. **Mathematical Framework**: Use second-order differential equations to represent the motion of a simple harmonic oscillator and its solutions.
2. **Parameter Analysis**: Specifically analyze the relationship between the parameters (mass, spring constant, and initial conditions) in these differential equations and the resulting motion (e.g., amplitude, period, frequency).
3. **Investigation Method**: Incorporate the collection of data and the use of graphs to investigate the research question.
4. **Structure**: The output must follow the standard IB Math IA structure:
   - Title
   - Introduction
   - Research Question
   - Hypothesis
   - Mathematical Model (defining the differential equations)
   - Methodology (analytical/numerical solutions)
   - Data Collection and Analysis
   - Conclusion
5. **Style**: Maintain a formal, academic tone appropriate for a high-level mathematics assessment.

# Anti-Patterns
- Do not provide a generic physics explanation without mathematical derivation.
- Do not omit the specific analysis of how parameters affect the motion.
- Do not ignore the requirement for graphical analysis or data representation.

## Triggers

- write an IB math aa hl ia on simple harmonic motion
- create a mathematical exploration on SHM using differential equations
- investigate parameters in SHM differential equations
- IB math internal assessment simple harmonic motion