I’ll create a physics simulation of a damped harmonic oscillator, which is a fundamental system in mechanics that appears in many real-world situations like spring systems, pendulums, and electrical circuits.
1 | import numpy as np |
Let me explain this physics simulation in detail:
Physical System:
- Damped harmonic oscillator (like a mass on a spring with friction)
- Governed by equation: $m(d²x/dt²) + c(dx/dt) + kx = 0$
- Parameters:
- Mass $(m) = 1.0 kg$
- Spring constant $(k) = 10.0 N/m$
- Damping coefficient $(c) = 0.5 Ns/m$
Visualization Components:
Position and Velocity vs Time:
- Shows oscillatory motion
- Demonstrates amplitude decay due to damping
Phase Space Plot:
- Shows system trajectory in position-velocity space
- Spiral pattern indicates energy dissipation
Energy Analysis:
- Shows kinetic and potential energy exchange
- Total energy decreases due to damping
Power Spectrum:
- Shows frequency components of motion
- Peak at natural frequency
System Parameters: Mass: 1.0 kg Spring Constant: 10.0 N/m Damping Coefficient: 0.5 Ns/m Natural Frequency: 3.16 rad/s Damping Ratio: 0.25
Physical Insights:
- Oscillatory motion with decreasing amplitude
- Energy transfer between kinetic and potential forms
- Damping causes energy dissipation
- Natural frequency determines oscillation rate
Key Features:
- Solves differential equations numerically
- Calculates system energies
- Provides multiple visualization perspectives
- Analyzes frequency components