First-Order ODE & Transient Relaxation Lab

Interactive step response and exponential relaxation simulator for first-order linear ordinary differential equations, modeling RL inductors, RC capacitors, and Newton's law of cooling with real-time 1τ (63.2%) and 5τ settling metrics.

Instrument State:Live Analytical DSP Engine

Calibrating DSP Instrument Pipeline...

Technical Instrument Specifications

Governing ODEdy/dt + P(t)y = Q(t) with IF = exp(∫ P dt)

Step Solutiony(t) = y_ss + (y_0 - y_ss) · exp(-t / τ)

Time Constantτ = L/R (RL), τ = RC (RC), τ = 1/k (Cooling)

Key Milestones1τ (63.2% rise), 2.2τ (10-90% rise), 4.6τ (99% settled)

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