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CLAUDE.md

This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.

Project Overview

This is a physics education simulation that visualizes the normal modes of a 1D coupled oscillator system. The system consists of N masses connected by springs between two fixed walls, demonstrating classical mechanics concepts for PHY313.

Running the Simulation

# Display animation interactively
python normal_modes.py

# Save animation to file (requires ffmpeg)
python normal_modes.py --outfile normal_modes.mp4

# Customize output settings
python normal_modes.py --outfile output.mp4 --fps 30 --dpi 150

Command line options:

  • --outfile FILENAME: Save animation to file instead of displaying (requires ffmpeg)
  • --fps FPS: Frames per second for output video (default: calculated from dt as 1/dt = 50)
  • --dpi DPI: Resolution for output video (default: 100)

The script creates an animated matplotlib visualization showing each normal mode sequentially, with each mode displayed for 4 seconds before transitioning to the next.

Physics Model

The system simulates N equal masses (default: 9) connected by equal springs with fixed boundary conditions:

  • Mode frequencies: ω_n = 2ω₀ sin(nπ/(2(N+1))) for n = 1, 2, ..., N
  • Mode shapes: The displacement of mass j in mode n is proportional to sin(n·j·π/(N+1))
  • Eigenvectors are normalized to have maximum displacement of 1

Key Parameters (normal_modes.py:7-21)

  • N: Number of masses (line 8)
  • m, k: Mass and spring constant (lines 9-10)
  • L: Total system length (line 14)
  • dt, t_per_mode: Animation time step and duration per mode (lines 19-20)
  • amplitude: Oscillation amplitude (line 39)

Code Structure

The simulation has three main sections:

  1. Physical setup (lines 7-36): Defines system parameters, calculates mode frequencies analytically, and constructs normalized eigenvector matrix
  2. Visualization setup (lines 41-77): Creates matplotlib figure with Circle artists for masses, line artists for springs, and Rectangle patches for walls
  3. Animation loop (lines 98-134): Updates mass positions and spring geometry each frame using displacements = amplitude * modes[:, current_mode] * sin(ω*t)

The draw_spring() function (lines 79-88) renders springs as zigzag patterns that compress/extend as masses move.

Modifying the Simulation

  • To change the number of masses, modify N at line 8
  • To adjust animation speed, change dt (line 19) or interval parameter in FuncAnimation (line 139)
  • Mass and spring visual sizing automatically scales with mass_spacing (lines 50-51)