Calculus
Lab: oscillations and second order
A mass, a spring and two initial conditions: compare regimes, inspect the graph and follow motion step by step.
Model and initial data
One second between steps; the slider shows simulated physical time. The spring drawing uses an illustrative scale adapted to the graph.
Motion of the mass
Displacement over time
Value table
Ideal linear model with m,k>0 and c≥0. Floating-point arithmetic; forced damped cases are approximate, without certified error bounds. Nearly critical classification is affected by numerical precision. Not a real-system design tool.