Damped Oscillation: Understanding Phase Difference

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Discussion Overview

The discussion centers around the concept of damped oscillation and phase difference in resonance, particularly in relation to pendulums. Participants explore the relationship between the natural frequency of oscillation, driving frequency, and phase difference, as well as the implications of these relationships in the context of resonance.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses confusion regarding the phase difference in resonance oscillation, questioning how a phase difference of T/4 can exist if the frequencies are the same.
  • Another participant states that at the resonant frequency with optimal damping, the phase difference is π/4, suggesting this does not contradict resonance since it is the point of maximum amplitude.
  • A different viewpoint is presented, indicating that while objects resonate, driving forces do not necessarily need to be in phase with the resonating object unless they are directly influencing it. The concept of phase lag due to system response is introduced.
  • One participant proposes the idea of two resonance conditions: one for an individual pendulum and another for a coupled two-pendulum system, suggesting that coupling can lead to new resonance frequencies.
  • Several participants clarify that "friver" is likely a typo for "driver" and express their own confusion regarding terminology.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of phase difference in resonance. There are multiple competing views regarding the relationship between driving forces and resonating objects, as well as the nature of resonance in coupled systems.

Contextual Notes

There are unresolved questions about the definitions and implications of terms like "driver pendulum" and "friver pendulum," as well as the conditions under which resonance and phase differences occur.

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In my notes, there are two sentences make me feel strange...

As we know, the pendulum whose length equals to that of the friver pendulum, its natural frequency of oscillation if the same of the frequency of the driving one. This is known as resonance oscillation.

However, somewhere I found another sentence...

"The resonant pendulum, is always a quarter of an oscillation behind the friver pendulu, i.e.there is a phase difference of T/4"

I don't know why there is a phase difference, if there is, then I think it contradicts the definition of resonance oscillation. :confused:
 
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In general, the phase difference is a function of the frequency and damping. At the resonant frequency, and at optimal damping ([tex]\gamma=w_0[/tex]), the phase difference is [tex]\pi/4[/tex].

This does not contradict the idea of resonance as this IS the frequency where the amplitude is maximum.
 
Objects resonate, and systems resonate, driving forces don't resonate, per se. I will have to look up this friver pendulum, but the driving point does not have to be in phase with an object at resonance unless it is directly driving the property of consideration. For instance, if you directly and rigidly grab the pendulum's cable and forcefully swing it back and forth, then you would need to stay in phase to induce resonance. If, however, you have a really loose spring attached to the driving point, then you have to take into account the delay in the spring. Delay in response at a certain frequency is the same thing as phase lag.

I couldn't find anything about a friver pendulum. Can you explain what it is? BTW, if you meant "driver pendulum," then I appoligize. I'm not trying to make fun of you or anything. Even if you did mean driver pendulum, I still don't quite have a picture in my mind of the set-up.

Something that just came to mind:
There may be two resonance conditions. One is the resonance of an individual pendulum and the other is the resonance of a coupled two-pendulum system. Even if these two pendulums have the same resonance frequency, their coupling can give you a new resonance frequency. In fact, there will be two natural frequencies for the coupled two-pendulum system.
 
Last edited:
I thought 'friver' was a typo for 'driver' !
 
right... driven = driving in my notes...i feel troublesome with these words too...
 
Well, I don't know what a driver pendulum is. Please explain.
 

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