A Damped Oscillator and Negative Damping Force

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Discussion Overview

The discussion revolves around the concept of a damped oscillator, specifically examining the relationship between the damping force and the rate of energy dissipation in the system. Participants explore the implications of negative damping forces and their effects on energy conservation within the context of oscillatory motion.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants assert that damping inherently means the force opposes motion, questioning the concept of a negative damping force as either confusing or redundant.
  • One participant suggests that without damping, oscillations would be periodic and energy would remain constant, implying that damping is the sole cause of energy loss.
  • A participant seeks clarification on how to mathematically derive the negative damping force from the equation of motion, indicating a need for further exploration of the relationship between the terms in the equation.
  • Another participant notes that the kinetic and potential energy terms in the equation leave out a term that corresponds to the damping force, suggesting a connection between energy change and damping.
  • There is a mention of the appropriateness of the forum for the discussion, with some participants indicating that it may be more suited for a homework section.

Areas of Agreement / Disagreement

Participants express differing views on the concept of negative damping and its implications, indicating that multiple competing perspectives remain unresolved. There is no consensus on the interpretation of damping forces or the classification of the discussion.

Contextual Notes

Some assumptions about the definitions of damping and energy conservation are not explicitly stated, and the mathematical derivation of the damping force from the equation of motion remains unresolved.

Nanofan01
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A damped oscillator is described by the equation m(x'') + b(x') + kx = 0, where the damping force is given by F = -b(x'). Show that the rate of change of the total energy of the oscillator is equal to the (negative) rate at which the damping force dissipates energy.
 
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Hi there,

to me, damping intrinsically means that the force opposes motion. So if you have a negative damping force, it's either confusing, or redundant.

This also seems like a homework question, in which case it's not posted in the right forum.

It seems to me like you could use common sense for this question then match the math up to it. If there is no damping, that means that the oscillation will be periodically identical (like a sine wave). No energy will be lost. Once you add that damping, that is the only cause of dissipating energy.

If you calculate the total change in energy of that equation of motion, then do the same without the damping force, you should find that potential + kinetic will be constant. Therefore you can conclude that the damping term is solely responsible for the loss of energy.
 
dacruick said:
to me, damping intrinsically means that the force opposes motion. So if you have a negative damping force, it's either confusing, or redundant.

The force does oppose the motion (assuming b > 0).

m(x'') + b(x') + kx = 0
m(x'') + kx = - b(x') = F
 
It makes sense that the rate of change of the oscillator is equal to the negative damping force but how do you mathematically derive [-b(x')] from [m(x'') + b(x') + kx]?
 
Also, which would be the right forum?
 
Nanofan01 said:
It makes sense that the rate of change of the oscillator is equal to the negative damping force but how do you mathematically derive [-b(x')] from [m(x'') + b(x') + kx]?

the kinetic energy is described by the m(x'') term, and the potential energy is described by the kx term. That leaves one term out right? Which just so happens to be your answer.

And there is a specific forum for homework. I don't think you'll have too much trouble finding it if you look.
 

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