Harmonic oscillator with/without gravity

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Discussion Overview

The discussion revolves around the energy dynamics of a mass-spring system when subjected to gravity, specifically comparing the energy states of the system in vertical and horizontal orientations. Participants explore the implications of gravitational potential energy (PE) in conjunction with spring potential energy (PE) and seek to understand the overall energy changes in the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that when gravity is applied to a vertical mass-spring system, the energy appears lower, prompting a request for an explanation of this phenomenon.
  • Another participant suggests that the comparison of gravitational PE and spring PE is crucial, indicating that the gravitational PE decreases while the spring PE increases as the system reaches a new equilibrium position.
  • A participant observes that the decrease in gravitational PE is greater than the increase in spring PE, questioning if there is a general principle that states energy decreases when an external conservative force is applied.
  • Another response clarifies that the observed energy relationship holds true only when comparing the changes in PE as the mass moves to its new equilibrium, and mentions that the spring force will eventually surpass the gravitational force, suggesting that the system behaves similarly to a horizontal setup at the new equilibrium.
  • One participant expresses uncertainty about the existence of a general law regarding energy decrease in the presence of external conservative forces.

Areas of Agreement / Disagreement

Participants express differing views on the implications of gravitational force on the energy of the system, with some agreeing on the need to consider both types of potential energy, while others question the existence of a general law regarding energy changes in such scenarios. The discussion remains unresolved regarding the broader implications of these observations.

Contextual Notes

Participants acknowledge the importance of comparing changes in gravitational and spring potential energy, but the discussion does not resolve the assumptions regarding the nature of energy changes in the presence of external forces.

daudaudaudau
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If I have mass on a spring that is oscillating in a linear motion, this system has a certain energy. Now if we imagine the system to be aligned along the vertical, why is the energy lower when gravity is turned on? I can calculate it and see that it is correct, but what is the "explanation" ? Because, I mean, when gravity is turned on, the string is stretched further, so this should increase the energy.
 
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When the system is vertical, you must also consider gravitational PE along with spring PE. Compare the increase in spring energy (as it stretches to the new equilibrium point, say) with the decrease in gravitational PE.
 
Right, and I can see that the decrease in gravitational PE is larger than the increase in the spring PE. Is there some general "law" stating that whenever you apply an external conservative force to a system, the energy decreases?
 
daudaudaudau said:
Right, and I can see that the decrease in gravitational PE is larger than the increase in the spring PE.
That's only true if you compare the change in gravitational and spring PE as the masses lowers to its new equilibrium position. Since the gravitational force is constant, the spring force will soon overtake it. I don't see anything particularly significant about this. With respect to its new equilibrium point, a vertical spring+mass behaves similarly to a horizontal one.
Is there some general "law" stating that whenever you apply an external conservative force to a system, the energy decreases?
Not that I'm aware of.
 

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