Calculating Undamped Natural Frequency of a Cantilever Beam

[hwt]

Homework Statement

Hi.

I'm trying to work out the undamped natural frequency of a cantilever beam. The setup of the system is shown in the image below.

[URL]http://www.flickr.com/photos/56901717@N03/5249378659/[/URL]

Data:(all lengths measured from the hinge on the left of the beam)
Beam: m=1.946 kg, L=L1=815mm
Spring: m=0.134 kg, at length L3=815mm
Motor block: m=5.250 kg at L4=264mm

4 blocks of 50g mounted on motor at e=32mm from centre of rotation.
k=430 N/m

Homework Equations

The Attempt at a Solution

We began by finding the experimental undamped frequency from our plot from the oscilloscope.

F=1/T this gave a result of 2.74Hz = 0.437 rad/s

I then use the summation of moments about the hinge (say point O) to find an equation for natural frequency:

[URL]http://www.flickr.com/photos/56901717@N03/5250100964/in/photostream/[/URL]

My problem comes when calculating moment of inertia, Io:

I have tried using the equation:

Io = (mL^2)/12 + mL^2

However I don't think this is right as I get
omega = 7.0806 which is much much higher than my initial value.

Could someone please indicate where I am going wrong so I can have another attempt at this!

Thanks!

 

[hwt]

I couldn't use the in built formula editor too well so a knocked up the formula in word and saved it as an image. I think you may just have to right click on the image and copy the URL to see them!

Thanks for your help