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Natural frequency of a simply supported beam

First natural frequency of a simply supported beam with a uniform mass, and the check against a floor vibration limit. Reference: Euler-Bernoulli beam theory.

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# Beam
E_m := 210 GPa
I_b := 8356e4 mm^4
L_s := 6 m
m_b := 450 kg/m

# Frequency
f_1 := pi/(2*L_s^2)*sqrt(E_m*I_b/m_b) = Hz
f_1 >= 3 Hz =
# A first frequency above about 3 Hz keeps a floor clear of resonance with walking; more detailed rules apply to sensitive floors.

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