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**[SOLVED] Cantilever Investigation**

**1.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 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.

**2. I have found these two formulae: (Shown much more clearly in attachments)**

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

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

**3. 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.

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.