Spring Constant

(1)     

where:

F is the static force and

is the displacement.

The spring constant can be estimated by using Beam Theory. Because the double beam apparatus has upper and lower beams that differ in composition will derive equations that will give the stiffness of one beam of the double beam apparatus. Once we know the relationships for one beam, we will then combine the stiffnesses of each beam to find the composite (or total) stiffness.

It can be shown that the equation for the spring constant of one beam is given by:

(2)     

where:

E is Young's Modulus,

I is the moment of inertia, and

L is the Length of the beam.

For the two beam apparatus, the total spring constant may be estimated by summing the spring constants of each beam. The total beam spring constant is given by:

(3)     .