A mass attached to two springs with different k values

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Discussion Overview

The discussion revolves around the mechanics of a mass attached to two springs with different spring constants (k values) and how to determine the effective spring constant when measuring the frequency of oscillation. The scope includes conceptual understanding and mathematical reasoning related to spring systems.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires whether the effective spring constant should be calculated as if the springs are in series or in parallel.
  • Another participant suggests considering the total restoring force when the mass is displaced from equilibrium, proposing a formula for the force based on the individual spring constants.
  • A participant confirms their understanding that the total force can be expressed as F = -k1x - k2x, leading to the conclusion that k = k1 + k2.
  • A later reply encourages further exploration of the scenario if the springs were connected in series.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to calculating the effective spring constant, with some proposing a parallel model while others suggest further investigation into the series configuration. The discussion remains unresolved regarding the optimal method for combining the spring constants.

Contextual Notes

Participants have not fully explored the implications of the springs being in series versus parallel, and there may be assumptions regarding the linearity of the springs that are not explicitly stated.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics, particularly those interested in mechanics and oscillatory systems.

darrenhb
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Hey. Suppose a mass is attached to two springs, one on each side, and they have different values for k. If you wanted to measure the frequency, how would you add up the k values? Would it work as if they were in series, so 1/k = 1/k1 + 1/k2, or would it just be k = k1 + k2 like in parallel? Or something else?

Thanks!
 
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See if you can figure it out. Imagine the mass pushed a distance X from equilibrium. What's the total restoring force from the two springs?
 
What I figured was that it would be F = -k1x - k2x, and therefore k = k1 + k2. Is this correct?

I always over-think these things!
 
darrenhb said:
What I figured was that it would be F = -k1x - k2x, and therefore k = k1 + k2. Is this correct?
You got it. :approve:

(Now you should figure out how things would be different if the springs were connected together in series.)
 
Thanks! I'll give that a go later, haha.
 

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