Is damped oscillation a kind of forced oscillation?

hydrogène

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?

dextercioby

You could say that,but the force would still be damped,even though periodic...

Daniel.

brewnog

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.

dextercioby

Yes,i agree,terminology & conventions would reccomend otherwise,but the mathematical structure is the same...

Daniel.

HallsofIvy

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.

Andrew Mason

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