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Parametric resonance is a situation where the driving frequency is a multiple of the eigenfrequency. Various people say that using a swing and propelling it oneself is such a case, with the driving frequency being the double of the eigenfrequency. But when I use a swing, as I did today, my own motion has the same frequency as that of the swing, not twice the frequency.

An example description is http://www.hk-phy.org/articles/swing/swing_e.html which claims that self-propelled swinging is normal resonance.

The opposite is said here: Wikipedia entry

What is the correct view: is self-propelled swinging normal resonance or is it parametric resonance?

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1 Answer 1

In the case of a father pushing a child, it's normal resonance.

In the case of a child driving the motion itself it's parametric resonance. The Wikipedia article you mentioned states: For example, a well known parametric oscillator is a child pumping a swing by periodically standing and squatting to increase the size of the swing's oscillations.

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Kvothe, I read that as well; but a child usually pushes with the same frequency as the swing; that is NOT parametric resonance. It is only parametric if it happens with double or threefold or fourfold etc frequency, if I understand correctly. –  Gianna Feb 9 at 12:12
Why do you think that? –  Kvothe Feb 9 at 13:30
Because of pages like elmer.unibas.ch/pendulum/parres.htm or also faculty.ifmo.ru/butikov/Applets/Par_resonance.pdf - am I misunderstanding them? –  Gianna Feb 9 at 18:38
Also the Wikipedia pages says: "Parametric resonance occurs in a mechanical system when a system is parametrically excited and oscillates at one of its resonant frequencies. Parametric resonance takes place when the external excitation frequency equals TWICE the natural frequency of the system. Parametric excitation differs from forcing since the action appears as a time varying modification on a system parameter. The classical example of parametric resonance is that of the vertically forced pendulum." –  Gianna Feb 9 at 18:43
@Gianna As far as I can see the big difference is the driving mechanism. If you forget about resonance for a moment, do you understand the fundamental difference between the two examples I listed in my answer? –  Kvothe Feb 9 at 20:09

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