Springs, dampers & damping

A spring pushes back in proportion to how far it's stretched — Hooke's law, F = −k·x (k = stiffness, N/m). A spring and a mass on their own form a perfect oscillator: displace it and it rings forever at its natural frequency:

ωₙ = √(k / m) (rad/s) → period T = 2π√(m / k)

A damper resists velocity instead of position — F = −c·v (c = damping coefficient, N·s/m). It converts motion into heat, so oscillations decay. How fast they decay is set by the dimensionless damping ratio:

ζ = c / (2√(k·m))

• ζ < 1 — underdamped: it oscillates, but the amplitude shrinks each cycle.
• ζ = 1 — critically damped: the fastest return to rest with no overshoot.
• ζ > 1 — overdamped: it crawls back to rest, no oscillation at all.

BriskFyr groups these as a component's law: linear elastic (spring only), linear viscous (damper only), and linear viscoelastic (both together) — one Spring/Damper/Spring-Damper component, three ways to configure it.

Build a spring–mass oscillator and see all three in Tutorial 4