Is damped oscillation a kind of forced oscillation?

AI Thread Summary
Damped oscillation and forced oscillation are distinct concepts in physics. A forced oscillation occurs when an external periodic force is applied to an oscillating system, while damped oscillation involves a damping force proportional to the system's velocity, which decreases amplitude over time. The damping force does not qualify as an external periodic force, as it is part of the system itself. Therefore, despite some mathematical similarities, damped oscillations are not considered forced oscillations. The key difference lies in the nature of the forces involved and their effects on the system's behavior.
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 reccomend 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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