Amplitude dependencies in an oscillator

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    Amplitude Oscillator
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Discussion Overview

The discussion revolves around the dependencies of amplitude in oscillatory systems, particularly in the context of a mass-spring system where a stone is released from a box. Participants explore the relationship between mass, amplitude, and energy in simple harmonic motion (SHM) and question how these factors interact during oscillations.

Discussion Character

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

Main Points Raised

  • One participant asserts that amplitude does not depend on mass, yet presents a scenario where changing mass appears to affect amplitude.
  • Another participant references the formula for angular frequency and the relationship between maximum speed and amplitude, suggesting that if mass changes but maximum speed remains constant, amplitude must also change.
  • A participant questions the initial conditions, pondering whether different initial masses might lead to confusion between SHM and simple pendulum behavior.
  • Discussion includes a comparison between mass-spring systems and pendulums, noting that the force in SHM depends on spring length, while in pendulums, it is proportional to mass.
  • One participant hints at the energy dynamics of the system when the stone leaves the box, suggesting that this may influence amplitude.
  • Another participant speculates that if the stone leaves the box at maximum extension with no kinetic energy, it could imply that amplitude does not change.
  • A participant challenges the idea that the stone has taken energy from the system, questioning what actually changes in the oscillation amplitude.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between mass and amplitude, with no consensus reached on how these factors interact in the given scenario. The discussion remains unresolved regarding the implications of mass change on amplitude in this specific context.

Contextual Notes

Participants reference various assumptions about energy conservation and the conditions under which the stone leaves the box, but these assumptions are not fully explored or resolved in the discussion.

malignant
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I know amplitude doesn't depend on mass but I came across a problem where the amplitude changed with a change in mass.

The problem was a horizontal frictionless spring with a box of mass m1 attached to it with a stone of mass m2 inside of the box. At its equilibrium point at its maximum speed, the stone left the box and the amplitude got smaller.

I'm confused as to why it changed? I can post the problem if it's not enough information.
 
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What do you mean by the amplitude doesn't depend on the mass?
Look at the formula for the angular frequency

\omega = \sqrt{\frac{k}{m}},

and look at the relationship between the maximum speed and the amplitude

v_{MAX}=\omega A

If the mass changes but the maximum speed doesn't, than the amplitude must change.
 
What about initially? Like not changing mass but different initial mass. Maybe I'm getting SHM mixed up with simple pendulums.
 
malignant said:
Maybe I'm getting SHM mixed up with simple pendulums.

For simple harmonic motion of a "mass on a spring", the force only depends on the change in length of the spring. The same force applied to a larger mass produces a smaller acceleration, and a lower oscillation frequency.

For a pendulum, the force also depends on the weight, which is of course proportional to the mass. So the acceleration of the mass, and the oscillation frequency of the pendulum, is independent of the mass.
 
malignant said:
I know amplitude doesn't depend on mass but I came across a problem where the amplitude changed with a change in mass.

The problem was a horizontal frictionless spring with a box of mass m1 attached to it with a stone of mass m2 inside of the box. At its equilibrium point at its maximum speed, the stone left the box and the amplitude got smaller.

I'm confused as to why it changed? I can post the problem if it's not enough information.

Clue: How does the energy in the oscillating system change when the stone leaves the box?
 
sophiecentaur said:
Clue: How does the energy in the oscillating system change when the stone leaves the box?

I think I see now. If the stone left the box when it was fully extended and there's no kinetic energy, then there isn't a mass variable, so would the amplitude not change then?
 
The box is in at the position of maximum extension so why would the amplitude of the oscillations change? The stone has 'taken' no energy from the system. So what actually will change?
 

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