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Quantum Engineering Year 0: Mathematical Foundations Month 3Day 69

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Year 0·Month 3·Week 2

Day 69: Computational Lab — Second-Order ODEs in Python

Day 69 of 2,016~10 min read

Learning Objectives

•Solve second-order ODEs symbolically with SymPy
•Solve second-order ODEs numerically by converting to systems
•Visualize oscillatory behavior and phase portraits
•Simulate damped and forced oscillations
•Analyze resonance computationally

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Setup Lab 1 Symbolic Solutions with SymPy 11 Homogeneous Equations 12 With Initial Conditions 13 Nonhomogeneous Equations Lab 2 Converting to First-Order Systems 21 The Key Transformation 22 Implementation Lab 3 Damped Oscillations 31 Three Damping Regimes 32 Phase Portraits for Different Damping Lab 4 Forced Oscillations and Resonance 41 Response to Forcing 42 Resonance Curve Amplitude vs Frequency 43 Resonance Animation Undamped Case Lab 5 RLC Circuit Simulation Lab 6 Quantum Harmonic Oscillator Lab Completion Checklist Lab Report Assignment Tomorrow Rest and Review

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