Stiffness of cantilever

[name218]

I am conducting an experiment to determine the stiffness constant of two cantilevers - (one with a wooden beam, and one with a plastic beam)

I am going to measure the period of oscillation of the beams with different masses on. From this I plan to determine the stiffness constant.

I thought of using the formula T = 2pi root(m/k). Is this formula suitable? I have been told this may be incorrect. Could there be another way to determine the stiffness constant using the mass and period of oscilaltion (I am not changing the length or anything else - just the mass)


After attempting to use this method, I have almost got a straight line graph of T squared against mass, however taking the recipricol of the gradient and multiplying it by 4pi squared give me a graph where the stiffness constand increases with mass, I thought this should now happen, I thought it should be the same regardless of the mass, is this true? Thanks

[Denise S.]

The formula is correct and you should obtain a straight line graph (allowing for experimental error), which does not pass through the origin, when you plot a graph of T^2 (s^2)) against m(kg). If you find the gradient of the best fit line then the elastic constant k(N/m) can be found by multiplying the reciprocal of this gradient by 4Pi^2. A second graph is not required.

You can compare this result with the value of k obtained by plotting a graph of F(N) where F=mg against the maximum deflection x(m) where k= gradient of this graph.

All this would have to be carried out for each material.

The elastic constant does not vary with mass it is constant until the physical dimensions and/or the material is changed.

[name218]

Thanks for your help Dennis

This should hopefully work now!

[Denise S.]

I cannot take any credit for this answer ! It is simply beyond me. My husband (Scotstone) is the brainy one but he forgot to re-register with HIS name.

It did deserve three stars didn't it?