Pendulum Simulation

An interactive physics simulation of a pendulum in different environments (Air, Water, and Vacuum) using Python and Pygame.

Overview

This project simulates a simple pendulum's motion in three different environments, demonstrating key physics concepts such as:

• Simple harmonic motion
• Damping effects in different media
• Energy conservation and transformation
• Interactive physics manipulation

Features

• Multiple Environments:
  • Air: Slight damping (0.999)
  • Water: Significant damping (0.95)
  • Vacuum: No damping (1.0)
• Interactive Controls:
  • Click and drag to manipulate the pendulum
  • Adjust pendulum length using arrow keys
  • Reset pendulum position with spacebar
  • Switch environments using number keys (1, 2, 3)
• Real-time Physics:
  • Accurate pendulum motion simulation
  • Visual trail of pendulum movement
  • Environment-specific visual effects
• Visual Feedback:
  • Real-time angle and velocity display
  • Environment-specific backgrounds
  • Pressure gauge in vacuum mode
  • Water surface effects in water mode

Physics Background

1. Simple Pendulum Motion

The pendulum follows the classic simple pendulum equation:

θ'' = -(g/L)sin(θ)

where:

• θ is the angle of displacement
• g is gravitational acceleration (9.81 m/s²)
• L is the length of the pendulum

2. Damping in Different Media

The simulation models different levels of energy loss:

• Air: Very slight damping (0.999)
• Water: Significant damping (0.95)
• Vacuum: No damping (1.0)

3. Energy Conservation

The pendulum continuously converts between:

• Potential Energy: U = mgh = mgL(1 - cos(θ))
• Kinetic Energy: K = ½mv² = ½mL²ω²

Installation

1. Ensure you have Python 3.x installed
2. Install required packages:

pip install pygame

Usage

Run the simulation:

python main.py

Controls

• 1: Switch to Air environment
• 2: Switch to Water environment
• 3: Switch to Vacuum environment
• Left/Right Arrow: Adjust pendulum length
• Space: Reset pendulum position
• Mouse: Click and drag to manipulate pendulum
• ESC: Quit simulation

Project Structure

• main.py: Main simulation loop and user interface
• pendulum.py: Pendulum physics implementation
• decoration.py: Visual effects and environment rendering
• constants.py: Simulation constants and configuration

Limitations

• The damping coefficients are simplified models and not based on actual experimental data
• The simulation uses basic Euler integration for physics calculations
• Air and water resistance are modeled using simplified damping factors

Acknowledgments

• Pygame library for graphics and user input handling
• Physics principles based on classical mechanics
• Inspired by educational physics simulations