Period of oscillation for a mass on a spring

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Discussion Overview

The discussion revolves around the factors influencing the period of oscillation for a mass attached to a spring, comparing it to a simple pendulum. Participants explore why mass appears to play a different role in these two systems, focusing on the mechanics of spring deflection and restoring forces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the period of oscillation for a mass on a spring depends on its mass due to the proportionality of spring deflection to the attached mass.
  • Others argue that for small masses, the spring does not deflect significantly, resulting in shorter oscillation periods compared to larger masses.
  • One participant points out that the restoring force for a pendulum is influenced by gravity, suggesting that larger masses lead to larger restoring forces, which is not the case for mass-spring systems.
  • A later reply challenges the idea that the period depends on spring deflection, stating that the period is independent of amplitude and that amplitude is determined by initial conditions rather than mass.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mass, spring deflection, and oscillation period, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations in the assumptions regarding the relationship between mass, amplitude, and period, as well as the specific conditions under which these principles apply.

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Why does the period of oscillation for a mass on a spring depend on its mass? (while in other situations, like a simple pendulum, the mass seems to be unimportant)
 
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Reason is the amount of spring deflection is proportional to the attached mass. If mass is very small, the spring doesn't deflect very much and takes a much short time to complete a cycle than if the mass was large.
 
because the restoring force for a pendulum is due to gravity
for a larger mass the restoring force is automatically larger.
that is not the case for a mass-spring system
 
hotvette said:
Reason is the amount of spring deflection is proportional to the attached mass. If mass is very small, the spring doesn't deflect very much and takes a much short time to complete a cycle than if the mass was large.
This is a little confusing and mostly not true.
The period does not depend on the spring deflection (amplitude) and the amplitude does not depend on the mass attached but on the initial conditions.
If you have in mind a vertical spring (it does not have to be vertical) with a mass attached, then the mass determines the equilibrium deflection, but this is not in general related to the amplitude or the period of the oscillations.
 

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