🌊 Wave Pendulum Simulation – NEDUET Physics

This web-based interactive simulation demonstrates the physics of pendulum waves. Created using pure HTML, CSS, and JavaScript, it visualizes the motion of multiple pendulums of varying lengths and simulates wave-like interference patterns over time.

✅ Created by: Huzaifa Ahmed Khan 👩‍🏫 Under the Supervision of: Ms. Marium Ghulam Nabi 🏫 Department of Physics, NED University of Engineering & Technology

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🧠 Physics Behind the Simulation

The motion of each pendulum follows the classical harmonic equation:

$$ \theta(t) = \theta_0 \cos\left(\sqrt{\frac{g}{L}} , t\right) $$

Where:

• $\theta(t)$ – Angular displacement at time $t$
• $\theta_0$ – Initial angle
• $g$ – Gravitational acceleration
• $L$ – Length of pendulum

By using pendulums of slightly varying lengths, their oscillations fall in and out of phase, creating beautiful wave-like patterns.

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🛠 Features

• 🎛️ Adjustable parameters:

  • Number of pendulums
  • Shortest & longest pendulum length
  • Gravity
  • Initial angle

• 🎨 Toggle motion trails for visual effects

• 📈 Real-time graph of $\theta(t)$ for the first pendulum using Chart.js

• 📤 Export graph data as:

  • PNG image
  • CSV data

• 📱 Responsive UI (scales well on various screen sizes)

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📂 File Structure

wave-pendulum-simulation/
│
├── index.html       # Main simulation page
├── style (inline)   # Embedded CSS styling
└── script (inline)  # JS logic for pendulum physics, animation & charting

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🚀 Getting Started

✅ Prerequisites

No installations or builds needed. This simulation is pure HTML/CSS/JS.

▶️ Run Locally

1. Clone this repository

   git clone https://github.com/your-username/wave-pendulum-simulation.git

2. Open index.html in any modern browser

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🧪 Technologies Used

• HTML5
• CSS3
• JavaScript (ES6+)
• MathJax – for LaTeX math rendering
• Chart.js – for plotting angular motion

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📤 Exports

• Export PNG: Download the graph as a .png image
• Export CSV: Download time-angle data for further analysis

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📜 License

This project is for academic and educational purposes. Contact the author if you'd like to reuse or build upon this work.

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