Is damped oscillation a kind of forced oscillation?

In summary, a forced oscillation is when a periodic force is imposed on an oscillating system. A damped oscillator has a damping force proportional to velocity, but it is not considered a forced oscillation because the force is not coming from an external source. Mathematically, a damped oscillation is different from a forced oscillation in terms of the period and amplitude of the force.
  • #1
hydrogène
8
0
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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  • #2
You could say that,but the force would still be damped,even though periodic...

Daniel.
 
  • #3
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.
 
  • #4
Yes,i agree,terminology & conventions would reccomend otherwise,but the mathematical structure is the same...

Daniel.
 
  • #5
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.
 
  • #6
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
 

Related to Is damped oscillation a kind of forced oscillation?

1. What is damped oscillation?

Damped oscillation is a type of oscillation where the amplitude of the oscillations decrease over time due to the presence of a damping force.

2. What is forced oscillation?

Forced oscillation occurs when an external force is applied to a system, causing it to oscillate at a frequency that is different from its natural frequency.

3. Is damped oscillation a type of forced oscillation?

Yes, damped oscillation is a type of forced oscillation because it occurs when an external force is applied to a system, causing it to oscillate at a different frequency from its natural frequency.

4. How is damped oscillation different from forced oscillation?

Damped oscillation differs from forced oscillation in that the amplitude of the oscillations decreases over time in damped oscillation, while the amplitude remains constant in forced oscillation.

5. What are some real-life examples of damped oscillation?

Some examples of damped oscillation in real life include a swing gradually slowing down due to air resistance, the vibrations of a car suspension system after hitting a bump, and the vibrations of a guitar string after it is plucked.

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