Damped Harmonic Oscillator Simulation ⚙️

This repository contains C programs that simulate a damped harmonic oscillator, a fundamental concept in physics and engineering. The simulations model the motion of a mass-spring-damper system using 3 different numerical integration methods to solve the second-order ordinary differential equation (ODE) of motion.

• Explicit Euler Method
• Euler-Cromer Method
• Runge-Kutta RK4 Method

Each method computes the position of the mass over time and outputs the results to a separate data file for analysis and visualization.

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🧠 Methods Overview

1. Explicit Euler Method

A simple first-order integration technique. It updates the position using the velocity from the previous time step. Suitable for basic simulations but may become unstable for stiff or oscillatory systems.

• Source file: Euler.c
• Output: damped_oscillation_Euler.txt

2. Euler-Cromer Method

A modification of the Euler method that uses the updated velocity to compute the new position, offering improved stability for oscillatory systems.

• Source file: Euler-Cromer.c
• Output: damped_oscillation_Euler_Cromer.txt

3. Runge-Kutta RK4 Method

A fourth-order integration method that evaluates the system at multiple intermediate points within each time step, providing much higher accuracy.

• Source file: Runge-Kutta-RK4.c
• Output: `damped_oscillation_RK4.txt

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🚀 Getting Started

To run these simulations, you will need a C compiler (like GCC) installed on your system.

Compiling and Running

1. Clone the repository

2. Compile the Euler.c program:

   gcc Euler.c -o euler

3. Compile the Euler-Cromer.c program:

   gcc Euler-Cromer.c -o euler-cromer

4. Run the Euler simulation This will generate a file named damped_oscillation_Euler.txt with the simulation data.

5. Run the Euler-Cromer simulation This will generate a file named damped_oscillation_Euler_Cromer.txt with its data.

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📂 Files

• Euler.c — Explicit Euler method implementation
• Euler-Cromer.c — Euler-Cromer method implementation
• Runge-Kutta-RK4.c — Runge-Kutta RK4 method implementation
• plot.py — Python script for result visualization
• damped_oscillation_Euler.txt, damped_oscillation_Euler_Cromer.txt, damped_oscillation_RK4.txt — Simulation outputs
• comparison_plot.png — Comparison plot of all methods

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📈 Visualization

The results from all three methods can be compared using the provided Python script:

• Plot script: plot.py
• Output plot: comparison_plot.png

python plot.py

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👩‍💻 Author

Lovingly crafted by Hanka Robovska 👩‍🔬

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📜 License

This project is licensed under the MIT License. For more details, see the LICENSE file.

Feel free to experiment with different physical parameters or time step values to observe how each method behaves!