# Screw critical speed
# Scope: Uniform simply supported circular shaft first bending mode; no axial load.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 1 m
diameter = 20 mm
modulus = 200 GPa
density = 7850 kg/m^3

area := pi*diameter^2/4 [m^2]
inertia := pi*diameter^4/64 [m^4]
critical := pi^2*sqrt(modulus*inertia/(density*area*length^4)) [rad/s]

check operating margin example: critical >= 1000 rpm

scenario alternative: length = 0.8 m