Spring Stiffness Constant

[name218]

What is the spring stiffness constant of wood and plastic? I am determining the stiffness constant of wood and plastic using an oscillating cantilever with the formula T = 2pi root(m/k)

[scotstone]

Assuming the mass(es) used is positioned at the free end of the cantilever, the spring stiffness of the cantilever(not the material) can be determined from:-

k = F/y where F = weight of mass(N) and y = max deflection(m).

OR if a series of masses has been used then k = gradient of a graph of F(N) against y(m)

The spring stiffness may also be calculated from:-

k = 3EI/L^3 where E is 11GPa(wood) or 2-4GPa(plastic).

Hope this helps.

[name218]

Would I have any problems with the formala I am using. I am plannning on timing the period of oscillation of the cantilever with different masses on the end. (I presume that the stiffness constant will be the same regardless of the mass?)

Thanks
PS Do you know a rough figure of what the stiffness of wood and plastic should turn out to be?

[scotstone]

You should not have any problems determining the spring constant using the formula . I assume you are planning to measure the periodic time for different masses and plot a graph of m(kg) against T^2 (s^2) and multiply the reciprocal of the gradient by 4Pi^2 to give k.

The spring stiffness is a property of the cantilever (ie spring) not the material and is constant unless you alter the physical dimensions or the material.The elasticity of the material is specified by its Modulus of Elasticity.

Once you have fixed the length of the cantilever the periodic time of oscillation is dependent only on the mass on the end of the spring. There will be some difference in your experimental and calculated results because you are not taking the mass of the beam itself into account or the fact that you will have damping.

[scotstone]

Sorry that should read T^2 against m for the graph.

[name218]

Thanks for your help scotstone, I have got a graph now, which isn't a staright line! (Which I presume it should be). I will try again anyway.