Spring-Mass System Simulation

Project Overview

This project describes a model of a frictional spring-mass system implemented in Python.

Project Structure

V SPRING-MASS-FRICTION-ANALYSIS
├── figures
│   ├── cycle_vs_position-img0.png
│   ├── cycle_vs_position.pdf
│   ├── cycle_vs_position.pgf
│   ├── displacement_vs_time_and_velocity_vs_displacement.pdf
│   ├── time_complexity.pgf
│   └── time_memory_complexity.pgf
├── bibtex.bib
├── configurations.tex
├── main.pdf
├── main.py
├── main.tex
└── rowdata.tex

Prerequisites

• Python 3.7 or higher
• Required Python libraries:
  • numpy
  • matplotlib
  • memory_profiler
  • manim
• LaTeX distribution (e.g., TeX Live, MiKTeX)

Installation

    git clone https://github.com/your-username/spring-mass-system-simulation.git
    cd spring-mass-system-simulation
    
    pip install numpy matplotlib memory_profiler manim

    python code/simulation.py
    
    python code/plotting.py

    python code/manim_simulation.py
    
    pdflatex main.tex
    biber main
    pdflatex main.tex
    pdflatex main.tex

Output Files

• figures/cycle_vs_position.pdf: Plot of cycle vs position.
• figures/displacement_vs_time_and_velocity_vs_displacement.pdf: Plot of displacement and velocity over time.
• figures/time_complexity.pgf: Plot of time complexity.
• figures/time_memory_complexity.pgf: Plot of time and memory complexity.

Sample Outputs

Displacement and Velocity Plot

Time Complexity Plot

Time and Memory Complexity Plot

References

• Smith, J. (2020). Introduction to the Spring-Mass System. Journal of Mechanics, 34(2), 123-145.
• Doe, J. and Brown, A. (2021). Advanced Oscillatory Motion. Springer.
• Johnson, L. (2019). Friction and Its Effects on Motion. Physics Today, 56(7), 78-90.
• Miller, R. (2022). Numerical Simulation Techniques. Wiley.
• Various other sources as listed in the main document.