Finding the natural frequency of a steel beam

[hks118]

Homework Statement

I am trying to calculate the natural frequency of a steel beam.

Homework Equations

I=1/12*W*T^3
Volume= T*W*L
M₀=V*ρ
K=(3EI/L^3)
M_eff=(33/140)*M₀+M_end
ωn=√(k/M_eff)

The Attempt at a Solution

This should be a simple plug and chug problem but I can't see what I'm doing wrong.

L=0.4572m
W=0.026035m
T=0.006223m
E= 3*10^6
ρ=7850kg/m^3

M_end=.025kg


I=5.22848E-10

V=7.41E-05 m^3

M₀=5.81E-01

K=0.049237907

M_eff=2.43E-01

ω_n=0.450088787 Hz

But this is way off from my experimental value of around 20Hz. Everything is in kg and m.

 

[Liquidxlax]

Sorry to ask this , what is K and what is E? and their units

 

[obafgkmrns]

Your modulus of elasticity appears to have units of psi. Change it to N/m^2 & you'll fix your problem.

 

[qasio]

natural frequency = (square root)k/m

 

[SteamKing]

E for steel is 3*10^7 psi (30,000,000 psi) not 3,000,000 psi