Physical Principles & Mathematical Derivation
Air drag and pivot friction apply a retarding torque proportional to angular velocity ω, bleeding mechanical energy into thermal dissipation Eth until the bob comes to rest at the stable bottom equilibrium θ = 0.
Questions & Concepts
What physical equation governs Damped Pendulum & Mechanical Energy Dissipation Lab?
θ̈ + b·θ̇ + (g/L) sin θ = 0 — Air drag and pivot friction apply a retarding torque proportional to angular velocity ω, bleeding mechanical energy into thermal dissipation Eth until the bob comes to rest at the stable bottom equilibrium θ = 0.
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.