Finding Equations for Multiple Springs in Series

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SUMMARY

The discussion focuses on solving a static spring system involving three springs in series, with given stiffness values (K1=1N/m, K2=3N/m, K3=2N/m) and natural lengths (L1=3m, L2=1m, L3=2m). The total length of the compressed springs is 4m, leading to the equation for the total spring constant: 1/K(total) = 1/K1 + 1/K2 + 1/K3. Participants emphasize the need for simultaneous equations to derive individual spring compressions and highlight the importance of balancing forces at the junctions of the springs.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of simultaneous equations and methods such as elimination
  • Familiarity with static equilibrium concepts in mechanics
  • Basic grasp of compression and extension in spring systems
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  • Study the derivation of equations for springs in series and parallel configurations
  • Learn about the iterative method for solving simultaneous equations
  • Explore static equilibrium principles in multi-spring systems
  • Investigate practical applications of spring systems in engineering contexts
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Students studying mechanics, engineers working with spring systems, and anyone interested in solving static equilibrium problems involving multiple springs.

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Homework Statement



I have a static spring system with 3 springs holding 2 masses in place I have the spring stiffnesses (K1=1N/m k2=3N/m k3=2N/m) and natural lengths (L1=3m L2=1m L3=2m) and the total length of the compressed springs (x1+x2+x3=4m)

Homework Equations



1/K(total) =1/K1 + 1/K2 + 1/K3

The Attempt at a Solution



I know that I derive simultanious equations and use the iterative or elimination method to solve what the x individual values are but I don't know how to get the equations for 3 springs in series and I can't find a relavent reference in my textbook other than the total of sthe spring constant
 
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The forces have to balance at the point where any two springs meet. That's two equations. The sum of the compressions of each spring equals the total compression is the third equation.
 

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