---
id: "cb6daaaa-5ae6-444f-901a-8cfa24ec7901"
name: "IB Math AA HL IA Exploration on Simple Harmonic Motion"
description: "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."
version: "0.1.0"
tags:
  - "IB Math"
  - "Internal Assessment"
  - "Simple Harmonic Motion"
  - "Differential Equations"
  - "Mathematical Exploration"
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"
---

# 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