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Oscillating with max amplitude - what's this called? watch

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    Issit Natural frequency?

    ty
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    (Original post by nas7232)
    Issit Natural frequency?

    ty
    If we are talking about a spring being forced to oscillate by a driving frequency then its maximum amplitude would be at the resonant frequency. The natural frequency is the frequency it oscillates if left by itself. Dont know if that helps
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    (Original post by F1 fanatic)
    If we are talking about a spring being forced to oscillate by a driving frequency then its maximum amplitude would be at the resonant frequency. The natural frequency is the frequency it oscillates if left by itself. Dont know if that helps
    resonant frequency = natural frequency
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    (Original post by Bezza)
    resonant frequency = natural frequency
    No, that is no so.

    If a system is left to oscillate on its own under constraints of no external forces, that is the natural frequence.

    Although if this system is driven by an external system at a frequency equal to the natural frequency of the latter then it resonates. This is the highest frequency a system can reach and is called the resonant frequency.

    Newton.
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    (Original post by Newton)
    No, that is no so.

    If a system is left to oscillate on its own under constraints of no external forces, that is the natural frequence.

    Although if this system is driven by an external system at a frequency equal to the natural frequency of the latter then it resonates. This is the highest frequency a system can reach and is called the resonant frequency.

    Newton.
    You're saying that if you force a system to oscillate at it's natural frequency then resonance occurs, which is what I said isn't it? :confused:
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    (Original post by Bezza)
    You're saying that if you force a system to oscillate at it's natural frequency then resonance occurs, which is what I said isn't it? :confused:
    No, what you said is that the natural frequency equals resonant frequency which is not so, because you need to ADD the natural frequency to the natural frequency to reach resonant frequency.

    Newton.
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    (Original post by Newton)
    No, what you said is that the natural frequency equals resonant frequency which is not so, because you need to ADD the natural frequency to the natural frequency to reach resonant frequency.

    Newton.
    eh? which 2 natural frequency are you adding together?
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    (Original post by Bezza)
    eh? which 2 natural frequency are you adding together?
    I think he meant you need a driving force with the same frequency as the natural frequency of the freely oscillating body to reach resonant frequency (resonance).
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    (Original post by endeavour)
    I think he meant you need a driving force with the same frequency as the natural frequency of the freely oscillating body to reach resonant frequency (resonance).
    which is exactly what I said (or at least what I meant)

    F1 fanatic said resonance occurs in driven motion when the driving frequency is equal to the resonant frequency. I said that this resonant frequency has the same value as the natural frequency
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    (Original post by Bezza)
    which is exactly what I said (or at least what I meant)

    F1 fanatic said resonance occurs in driven motion when the driving frequency is equal to the resonant frequency. I said that this resonant frequency has the same value as the natural frequency
    If we are being picky the natural frequency is not necessarily the resonant frequency although this is suitable for A level. What messes it up is a dmping term if applicable so that the resonant frequency is no longer the natural frequency.

    So a solution of:

    d^2x/dt^2 + w^2 x = 0 does give a resonant frequency of w which is the natural frequency. However with a damping term:

    d^2x/dt^2 +(gamma)dx/dt + w^2 x = 0

    the resonant frequency is in fact given by the solution of the auxillary root eqn and gives:

    (1/2)(gamma^2 - 4w^2)^(1/2) which is not in general equal to w and so the resonant frequency for the system is not the natural frequency. However al that was pointless as at A level you ignore damping and so they are the same
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    (Original post by F1 fanatic)
    If we are being picky the natural frequency is not necessarily the resonant frequency although this is suitable for A level. What messes it up is a dmping term if applicable so that the resonant frequency is no longer the natural frequency.

    So a solution of:

    d^2x/dt^2 + w^2 x = 0 does give a resonant frequency of w which is the natural frequency. However with a damping term:

    d^2x/dt^2 +(gamma)dx/dt + w^2 x = 0

    the resonant frequency is in fact given by the solution of the auxillary root eqn and gives:

    (1/2)(gamma^2 - 4w^2)^(1/2) which is not in general equal to w and so the resonant frequency for the system is not the natural frequency. However al that was pointless as at A level you ignore damping and so they are the same
    The equations you're solving are the equations of motion of a particle on it's own (ie without a driving frequency), so the solutions will give the natural frequencies of those systems, won't they? So isn't the natural frequency of the system with damping equal to the resonant frequency of this system?
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    Agree with Bezza that natural frequency = resonant frequency. When frequency of the force applied = natural frequency, resonance occurs
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    The different between them is: The natural frequency is a porperty of the system, whereas resonant frequency is the frequency of the force when we try to make it as close to natural frequency as possible.
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    (Original post by Bezza)
    The equations you're solving are the equations of motion of a particle on it's own (ie without a driving frequency), so the solutions will give the natural frequencies of those systems, won't they? So isn't the natural frequency of the system with damping equal to the resonant frequency of this system?
    I solved the complementary solution which gives the SHM dependence of the equation. It is this which determines the resonant frequency. The particular integral will naturally have to be equal to this frequency for resonance. ie it would have to be sinusoidal with the frequency I gave. Of course all this is by the by given we are talking A level. The natural frequency of a spring is still w though. Im pretty sure it is anyway.

    As a correction I take your point about w. w is the frequency were damping not present. And so in this particular case you are correct. The thing is in general we do not know gamma and so we assume the natural frequency to be w and so the resonant frequency would not be over the natural frequency but slightly displaced. The joy of physics is that its all models & assumptions :rolleyes:
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    (Original post by F1 fanatic)
    I solved the complementary solution which gives the SHM dependence of the equation. It is this which determines the resonant frequency. The particular integral will naturally have to be equal to this frequency for resonance. ie it would have to be sinusoidal with the frequency I gave. Of course all this is by the by given we are talking A level. The natural frequency of a spring is still w though. Im pretty sure it is anyway.

    As a correction I take your point about w. w is the frequency were damping not present. And so in this particular case you are correct. The thing is in general we do not know gamma and so we assume the natural frequency to be w and so the resonant frequency would not be over the natural frequency but slightly displaced. The joy of physics is that its all models & assumptions :rolleyes:
    I thought you were saying that for a system, the resonant frequency was different to the natural frequency. The natural frequency of the spring will still be w, but the system obviously has a different natural (and therefore resonant) frequency.
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    driving the system with a speed equal to that of the natural frequency results in large amplitude violent vibrations. this is called resonance.

    similar things occur when the system is driven at a multiple of the natural frequncy. eg 2x, 3x, these are called 'harmonious frequencies' however the further departed the driving frequency is from the natural frequency,m the smaller the resonant effect
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    actully it depends ,maybe its the max displacement it depends on the situation the guy/girl did mention any example so we can say that it is the resonant frequency
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    resonance is when the driven frequency becomes equal to the natural frequency then during damping it's not resonant any more,
 
 
 

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