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Modelling System Parameters |
The spring constant can be measured directly in lab by
applying a known force (weight) to the end of the double beam apparatus and
measuring the displacement. Recall that the spring constant is defined as the
ratio of force over displacement and can be written as:
- 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
- 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
Last Updated: January 16, 2000, firstname.lastname@example.org
Copyright © 1993-1995, 2000, Pamela A. Eibeck and Brandon Muramatsu
Original WWW Conversion by Winston Wang, 1994
WWW ReConversion by Brandon Muramtasu, 2000