Simple harmonic motion springs

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Discussion Overview

The discussion revolves around the behavior of a spring-mass system undergoing simple harmonic motion (SHM). Participants explore the relationship between the amplitude of oscillation and the displacements caused by the mass and additional stretching of the spring. The conversation includes theoretical considerations and implications of different scenarios affecting the system's equilibrium and oscillation.

Discussion Character

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

Main Points Raised

  • One participant questions why the amplitude of oscillation is not the sum of the displacements due to the mass (X) and the additional stretching (Y), suggesting it is only Y.
  • Another participant proposes a scenario where if Y equals zero, the system would remain in equilibrium, implying that the amplitude would then equal X.
  • A further contribution discusses the nature of SHM, stating that the restoring force is proportional to the displacement from the equilibrium position, and that Y could be positive or negative based on the mass's position relative to X.
  • Another idea is introduced about the spring being partly open when unloaded, suggesting that the rest position of the mass would change, yet the restoring force per unit displacement would remain constant, leading to the same period of oscillation.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the displacements and the amplitude of oscillation, indicating that multiple competing perspectives exist without a clear consensus on the correct interpretation.

Contextual Notes

There are assumptions about the spring's behavior under different conditions, such as whether it is unloaded or how the mass affects the equilibrium position. The discussion does not resolve these assumptions or their implications for the system's dynamics.

Jas
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I have a spring with mass M attached, and leave it at equilibrium. Then I displace it some more by stretching it down a bit more. Displacement due to the mass= X, displacement due to stretching it even more=Y.

Why isn't the amplitude of oscillation= X+Y, but is only actually only Y? This is really confusing me!

Relevant equations: (L is the natural length of the spring, and x is the extension, λ is the modulus of elasticity
Tension=λx/L
Energy stored=λx^2/2L
 
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Jas said:
I have a spring with mass M attached, and leave it at equilibrium. Then I displace it some more by stretching it down a bit more. Displacement due to the mass= X, displacement due to stretching it even more=Y.

Why isn't the amplitude of oscillation= X+Y, but is only actually only Y? This is really confusing me!

Relevant equations: (L is the natural length of the spring, and x is the extension, λ is the modulus of elasticity
Tension=λx/L
Energy stored=λx^2/2L
What if ##Y = 0##?
 
PeroK said:
What if ##Y = 0##?
Then it would just stay in equillibrium
 
Jas said:
Then it would just stay in equillibrium

But you would have it oscillate with amplitude ##X+ Y = X##.
 
Jas said:
Why isn't the amplitude of oscillation= X+Y, but is only actually only Y? This is really confusing me!
The nature of SHM is that the restoring force is proportional to the displacement from the equilibrium (or rest) position. Y will be positive or negative, depending on whether the mass is above or below position X. We, of course, assume that the k of the spring is the same over the whole range of positions of the mass.
Here's another idea. Assuming the spring is partly open went unloaded (easy to arrange by giving it a good stretching!) Then imagine the spring and mass are laid on a frictionless horizontal surface ( dry, clean ice). The rest position of the mass will now be different, with respect to the fixing of the spring but the restoring force per cm of displacement will still be the same. So the period will be exactly the same as when the mass is hanging down. The amplitude will still be the maximum displacement relative to the rest position.
 

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