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Hi,

I am writing a report on cantilever oscillations, my experiment involves fixing different cantilvers e.g. a ruler to the end of a table then measuring the period and height of oscillations while varing the mass attached to the cantilever, and other varients e.g. lenght of cantilever.

I have come accross these two formulae:

T= 2(pi)*[(4ML^3)/(bd^3E)]^1/2

and:

h= 4MgL^3/Ebd^3

where: b= width of cantilever

d= thickness of cantilever

E= Youngs Modulus

M=Mass

L=Lenght of cantilever

T=period of oscillations

h=height of oscillation

I have looked at eqn's involving Hooke's and simple harmonic motion but cannot work out how these formulae have been derived.

Does anyone know how these formulae where derived, or where I can find information on this in general?

Thanks.

ash.

p.s. I have written out the formulae using math open office and attached them in pdf if it helps make them easier to read.

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# Cantilever experiment

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