In standard college physics text books, high-school books and popular level physics books, the collapse of the Tacoma Narrows Bridge is often taken as an example of resonance. However a more detailed analysis shows that the collapse was not due to simple resonance (see the article by Billah and Scanlan and Wikipedia).

Now my question is, whether there are further examples from mechanics, which are often incorrectly or oversimplified declared as examples of resonance phenomena (for example in physics text books)?

Edit: I should add, that the definition usually given in textbooks is the following: Consider a mechanical system which can be described by a differential equation like

$\frac{d^2}{d t^2}x(t) + 2 \rho \frac{d}{d t} x(t) + \omega_0^2 x(t) = f(t) $

where $f(t) = f_0 \cos(\omega t)$.

Then for example the amplitude or the energy of the system as function of $\omega$ has a maximum near $\omega_0$. In this case one speaks of resonance of the system.

  • 1
    $\begingroup$ Wikipedia is incorrect--- the vortex shedding frequency does not have to match the structural frequency exactly, it just has to have a Fourier component that does. Exactly 5 vortices were shed on each cycle of the bridge, and this is a condition for resonance, because the driving force has a component at the natural frequency. There is no other possible explanation, and "solving the coupled nonlinear equations" mentioned on Wikipedia is just the a way of saying "it's complicated". It's not complicated. It's resonance. $\endgroup$ – Ron Maimon Sep 16 '11 at 8:28
  • $\begingroup$ physics.stackexchange.com/questions/9582/… $\endgroup$ – user76940 Apr 4 '15 at 5:20

looking at the link you gave, I think it is just a problem of name convention and has nothing to do with oversimplifications.

It was indeed ruled out that the reason of the failure was not due to a resonance phenomenon called the Kármán vortex street,

Karman vortex street

a phenomenon arising in fluiddynamics with a certain resonance frequency, called the Strouhal frequency. However, if you look a little further you find that the cause for failure was due to aeroelastic flutter. According to the wikipedia article

Flutter is a self-feeding and potentially destructive vibration where aerodynamic forces on an object couple with a structure's natural mode of vibration to produce rapid periodic motion. Flutter can occur in any object within a strong fluid flow, under the conditions that a positive feedback occurs between the structure's natural vibration and the aerodynamic forces.

So, it is a kind of periodic process, driven by an excitation (here aerodynamic force) causing an energy flow into an eigenmode of the system possibly leading to destruction.
I think there is no problem calling this a resonance unless you give a very strict definition of such a process.

  • $\begingroup$ Do you have a reference of a university level physics textbook, where resonance is defined in this generality? $\endgroup$ – student May 8 '11 at 12:48
  • $\begingroup$ @student: No, I don't have a reference at hand. Remember that there are much more "resonances", e.g. the Fano one which is not explained by your assumed oscillator equation. Greets $\endgroup$ – Robert Filter May 8 '11 at 16:30
  • $\begingroup$ This is a good answer, but there is no definition of resonance which is so strict as to exclude this effect. The periodic process which drives energy into an Eigenmode must be nearly resonant with that Eigenmode, in that its period divides the Eigenmode period, so that it has a Fourier component which drives the resonance. $\endgroup$ – Ron Maimon Sep 16 '11 at 8:30

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