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.
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.
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:
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!
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