# Second-order response
# Scope: Canonical underdamped second-order overshoot; 0 < damping < 1.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

naturalFrequency = 10 rad/s
damping = 0.5

overshoot := exp(-pi*damping/sqrt(1-damping^2))
settling := 4/(damping*naturalFrequency) [s]

check overshoot budget: overshoot <= 0.2

scenario alternative: naturalFrequency = 8 rad/s