Justification for spring in series/parallel

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In summary, the conversation discusses finding the frequency of oscillation for a mass suspended by two springs with constants k1 and k2 in different configurations. The question asks why the constants add with reciprocal action for parallel configurations, and the individual was able to confirm this through logic and the internet. They are seeking a formal "proof" for this concept and have looked at the proof on Wikipedia, but are still trying to understand it. The individual has already solved the problem and just wants justification for their solution. After some time and effort, they were able to understand the concept.
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RubinLicht
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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
 
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  • #2
Took me a while, but i got it. thanks all.
 

1. What is the purpose of justifying the use of springs in series or parallel?

The justification for using springs in series or parallel is to increase the overall stiffness or flexibility of a system. By combining multiple springs in series or parallel, the resulting spring constant can be adjusted to fit the specific needs of the system.

2. How does the arrangement of springs in series or parallel affect the overall stiffness?

The arrangement of springs in series increases the overall stiffness of the system, while the arrangement in parallel decreases it. This is because in series, the springs are stacked on top of each other, requiring more force to compress them. In parallel, the force is distributed among the springs, resulting in a lower overall stiffness.

3. Can springs in series or parallel be used interchangeably?

No, springs in series and parallel cannot be used interchangeably. The arrangement of the springs affects the overall stiffness of the system, so using them interchangeably would result in a different response from the system.

4. How do I determine the overall spring constant when using springs in series or parallel?

When springs are arranged in series, the overall spring constant is equal to the sum of the individual spring constants. When springs are arranged in parallel, the overall spring constant can be calculated using the equation 1/k = 1/k1 + 1/k2 + ... + 1/kn, where k1, k2, etc. are the individual spring constants.

5. Are there any real-life applications where the use of springs in series or parallel is justified?

Yes, springs in series or parallel are commonly used in various mechanical systems such as suspension systems in cars, shock absorbers, and even in everyday objects like mattresses. They are also used in engineering designs to control the stiffness of structures or components.

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