Is damped oscillation a kind of forced oscillation?

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Discussion Overview

The discussion revolves around the relationship between damped oscillations and forced oscillations in oscillating systems. Participants explore definitions, mathematical representations, and the implications of damping forces in the context of periodic forces.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that since the damping force in a damped oscillator is proportional to velocity and varies periodically, it could be considered a periodic force, suggesting that damped oscillation might be a type of forced oscillation.
  • Others argue that a damped oscillation should not be classified as forced because the damping force is part of the system itself, not an external periodic force.
  • One participant notes that while the mathematical structure of damped and forced oscillations may appear similar, they are fundamentally independent concepts based on their definitions.
  • Another participant clarifies that in a forced simple harmonic oscillator, the period of the applied force is independent of the system's oscillation period, contrasting this with the characteristics of damped oscillations.

Areas of Agreement / Disagreement

Participants express differing views on whether damped oscillations can be classified as forced oscillations. There is no consensus, as some maintain that the definitions are distinct while others see potential overlap in the characteristics.

Contextual Notes

Participants highlight the importance of definitions in classifying oscillations, and there are unresolved nuances regarding the mathematical treatment of damping and forcing in oscillatory systems.

hydrogène
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I am confused!
Forced oscillation is the one which a periodic force is imposed on a oscillating system.
For a damped oscillator, the damping force is proportional to velocity which varies periodically. Does it mean that the damping force is a periodic force and the damped oscillation is a forced oscillation?
 
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You could say that,but the force would still be damped,even though periodic...

Daniel.
 
No, I wouldn't say that. I'd only call an oscillation forced if something outside the system is imposing that periodic force. A dashpot is part of the system, I would not consider it an external force.
 
Yes,i agree,terminology & conventions would recommend otherwise,but the mathematical structure is the same...

Daniel.
 
Mathematically the differential equation mx"+ cx+ kx= f(t) gives an "oscillatory" solution as long as the discriminant c2- 4mk< 0. A "damped" oscillation is one in which c> 0. A "forced" oscillation is one in which f(t) is not identically 0.

No, in that sense, "damped" and "forced" are completely independent.
 
hydrogène said:
I am confused!
Forced oscillation is the one which a periodic force is imposed on a oscillating system.
For a damped oscillator, the damping force is proportional to velocity which varies periodically. Does it mean that the damping force is a periodic force and the damped oscillation is a forced oscillation?
The period of the damping force is determined by the period of the oscillating system (ie they are equal) and the Amplitude is always decreasing (exponentially). In a forced simple harmonic oscillator, the period of the force is independent of the oscillating system and the amplitude is constant. So the damped oscillation is not a type of forced oscillation.

AM
 

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