Justification for spring in series/parallel

  • Thread starter Thread starter RubinLicht
  • Start date Start date
  • Tags Tags
    Spring
Click For Summary
SUMMARY

The discussion centers on the justification for the behavior of springs in series and parallel configurations, specifically focusing on the effective spring constant calculations. For springs in series, the effective spring constant is determined using the formula 1/K_eq = 1/k1 + 1/k2, while for parallel springs, the effective spring constant is simply the sum of the individual constants, K_eq = k1 + k2. The user sought a formal proof for the series configuration, having already confirmed their understanding through logical reasoning and external sources.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Familiarity with spring constant notation (k1, k2)
  • Basic knowledge of series and parallel circuit concepts
  • Ability to interpret mathematical proofs and equations
NEXT STEPS
  • Study the derivation of effective spring constants in series and parallel configurations
  • Learn about the physical implications of massless springs in oscillatory systems
  • Explore the relationship between spring constants and frequency of oscillation
  • Review advanced topics in mechanical oscillations and energy conservation
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for clear explanations of spring behavior in different configurations.

RubinLicht
Messages
131
Reaction score
8

Homework Statement


Find the frequency of oscillation of mass m suspended by two springs having constants k1 and k2, in each of the configurations shown.

my question isn't on how to solve the problem but rather why the constants add with reciprocal action for parallel. I was able to figure this out with just logic and confirmed it with the internet, but i would like a formal "proof", if you can call it that, for why it works.
assume massless springs.

Homework Equations


F=-kx
Series: 1/k1+1/k2=1/Keq

The Attempt at a Solution


nada, already solved the problem, just want justification. Thanks for the help

EDIT: i am reading the proof on wikipedia, but it'll still take a while for me to get it as my physical intuition is still trying to catch up with the math. Parallel is easy, got that. all that's left is series
 
Physics news on Phys.org
Took me a while, but i got it. thanks all.
 

Similar threads

Finding effective spring constants
  • · Replies 2 ·
Replies
2
Views
4K
Identifying Multiple Oscillations in a Graph
  • · Replies 19 ·
Replies
19
Views
3K
Classical mechanics:effective spring const
  • · Replies 9 ·
Replies
9
Views
3K
Why is W Tot not equal to W Glider on Spring in Newton's Third Law?
  • · Replies 3 ·
Replies
3
Views
2K
Springs in series and in parallel
  • · Replies 3 ·
Replies
3
Views
2K
Why is a negative spring constant unrealistic in this system?
  • · Replies 2 ·
Replies
2
Views
5K
Equivalent Spring Constant in Series and Parallel Configurations
  • · Replies 15 ·
Replies
15
Views
25K
Does Swapping Linear and Non-Linear Springs in Series Change System Behavior?
  • · Replies 3 ·
Replies
3
Views
2K
Statics Problem involving blocks, rope, pulleys and springs....
  • · Replies 2 ·
Replies
2
Views
3K
Frequency of an oscillating mass with springs in series
  • · Replies 1 ·
Replies
1
Views
14K