Displacement Curve Analysis for a Differential Equation Example

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Resource Overview

Implementation of displacement curve analysis, phase diagram plotting, power spectrum computation, Poincaré section visualization, and motion animation simulation for a differential equation system modeling spring-damper dynamics

Detailed Documentation

This example demonstrates the analysis of a differential equation system modeling object motion under spring and damper influences. The implementation involves numerical integration using Runge-Kutta methods to compute displacement curves, which track position variations over time. Phase diagrams are generated by plotting velocity against displacement, revealing system dynamics in state space. Power spectrum analysis utilizes Fast Fourier Transform (FFT) algorithms to identify dominant frequency components and system resonances. Poincaré sections are constructed by sampling phase-space trajectories at periodic intervals, effectively visualizing periodic motion patterns through stroboscopic techniques. The animation simulation employs real-time plotting functions with frame-by-frame updates, dynamically illustrating the mechanical system's motion through coordinate transformations and time-step propagation.

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