cotkhd
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What would the resonant frequency of a child on a swing be? Would it be the natural frequency of the swing itself, since if an external driving force at the same frequency of the natural frequency of the swing was applied, the resonant frequency would be achieved?

Correct me if I am wrong but the resonant frequency is the frequency at which maximum amplitude is achieved, and that must be when the driving frequency is in phase with the natural freq of the system
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Pidge Gunderson
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Resonant frequency would be the when the driving force (external) is at the same frequency as the natural frequency of the swing.
At this frequency, the amplitude of the swing would be at its highest, and the phase difference between the driving force and the oscillation of the swing is 90 degrees.
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cotkhd
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(Original post by Kyou)
Resonant frequency would be the when the driving force (external) is at the same frequency as the natural frequency of the swing.
At this frequency, the amplitude of the swing would be at its highest, and the phase difference between the driving force and the oscillation of the swing is 90 degrees.
Thank you. So was I correct?
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Pidge Gunderson
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(Original post by cotkhd)
Thank you. So was I correct?
Yep you were
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cotkhd
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(Original post by Kyou)
Yep you were
Awesome!
Also in my book it says:

''lightly damped systems have a very sharp resonance peak''- how is that so?
and

''the lighter the damping, the larger the maximum amplitude becomes at resonance''- how? and ''the closer the resonant frequency is to the natural frequency of the system'', also how?

Ive been trying to make sense of this for hours
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Pidge Gunderson
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(Original post by cotkhd)
Awesome!
Also in my book it says:

''lightly damped systems have a very sharp resonance peak''- how is that so?
and

''the lighter the damping, the larger the maximum amplitude becomes at resonance''- how? and ''the closer the resonant frequency is to the natural frequency of the system'', also how?

Ive been trying to make sense of this for hours
If they're lightly damped that means their amplitude will be higher then if they are heavily damped, won't it? So lightly damped systems will have a much sharper and higher resonance peak then heavily damped systems, which will have a less sharp and lower peak.

Damping is a phenomena which reduces the amplitude of oscillations due to energy being lost. So if the damping is lighter, less energy is lost from the system so the maximum amplitude it can achieve is larger.

The closer the resonant frequency is to the natural frequency, the higher the amplitude of oscillations.
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cotkhd
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(Original post by Kyou)
If they're lightly damped that means their amplitude will be higher then if they are heavily damped, won't it? So lightly damped systems will have a much sharper and higher resonance peak then heavily damped systems, which will have a less sharp and lower peak.

Damping is a phenomena which reduces the amplitude of oscillations due to energy being lost. So if the damping is lighter, less energy is lost from the system so the maximum amplitude it can achieve is larger.

The closer the resonant frequency is to the natural frequency, the higher the amplitude of oscillations.
Im sorry for being a pain in the ass but could you explain that very last ''the closer the resonant freq'' sentence in layman terms please
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Physics Enemy
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(Original post by cotkhd)
...
(Original post by Kyou)
...
Resonant freq is the freq that causes max amplitude of the swing for the damping level it experiences.

If undamped: resonant freq = natural freq, causing largest possible (and sharpest peaked curve) max amplitude.

If damped: resonant freq < natural freq, causing smaller (and flatter peaked curve) max amplitude. Matching natural freq causes even smaller amplitude!
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cotkhd
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(Original post by Physics Enemy)
Resonant freq is the freq that causes max amplitude of the swing for the damping level it experiences.

If undamped: resonant freq = natural freq, causing largest possible (and sharpest peaked curve) max amplitude.

If damped: resonant freq < natural freq, causing smaller (and flatter peaked curve) max amplitude. Matching natural freq causes even smaller amplitude!
How would the resonant frequency be smaller than the natural frequency for damped vibrations?
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Physics Enemy
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(Original post by cotkhd)
How would the resonant frequency be smaller than the natural frequency for damped vibrations?
Don't know why, but it is. More damped a system is, smaller the resonant freq (and max amplitude obv), thus greater the difference with natural freq.

See: http://2.bp.blogspot.com/-2WMrGtQ18N...12-51%2BPM.png
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