Resonance frequency of cantilever beam

[seang]

Homework Statement

Sorry for wasting your time and bandwidth, but I can't figure this out. I just have a cantilever beam with the following specifications:

length : 40 in.
width: 2 in.
height: 2 in.
E = 30e6 psi.
mbar = .8991 lbm/in.

And I'm trying to find the beam's resonance frequency (first mode). The problem is, I can't get a consistent answer between using SI units and the disastrous units given above.

Homework Equations

First I converted all of the above values to SI:

length = 1.016 m
width = .0508 m
height = .0508 m
E = 2.068e11 Pa
mbar = 15.878 kg/m

And I'm using the equation below to calculate the resonance frequency.

$$\omega = (1.875)^2 \sqrt{\frac{EI}{\overline{m}l^4}$$}}

where

$$I = \frac{wh^3}{12}$$

The Attempt at a Solution

If i do this, I get about 14.74 Hz for the imperial figures, and 289.6 Hz for the SI case. What gives? I have to be doing something wrong...

 

[SteamKing]

g = 386 in / s^2 seems to be missing

 

[seang]

How would that factor come about? I hvae converted all the imperial quantities as mentioned above, not sure where that factor would come in.

However, if I multiply my imperial figure by sqrt(386), I get about 262 Hz, which is somewhat close...

Thanks for your reply btw