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Most any quantum mechanics textbook will discuss molecular resonances. The classic book on molecular resonant frequencies is Spectra of diatomic molecules by Gerhard Herzberg. For larger molecules, you will want to consult Infrared and Raman spectra of polyatomic molecules, also by G. Herzberg. As for the microwave issue, the second link that you cite, ...


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What is important in the idea of resonance with water is to establish a frequency of excitation that causes the natural frequencies to superimpose or wave superposition. By achieving wave superposition the amplitude of the oscillations will have the greatest potential of breaking the molecule into its elemental constituents thereby creating free atoms that ...


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Decaying exponentials are the result of there being a fixed probability of any specific member of a population being removed. Once removed, the population decreases and so the rate of decay also decreases. The rate of decay is therefore associated with a particular time scale related to the change in population. The same model works if the population is ...


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A possible answer for that might be that if you have a rope with the length $L$, you have a frequency $f$ as the first harmonic frequency with $T=\frac{1}{f}$ as the time between two amplitude maxima. This time is determined by the frequency how fast the wave can propagate in the rope, and is therefore bound to the speed of sound in the rope $$\nu = ...


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Generally, in linear systems modes are independent. Energy does not flow from one mode to another. What causes the coupling is a nonlinearity. The nonlinearity reveals itself at higher amplitudes (nonlinear terms are small at small amplitudes). Thus, when you drive the rod just a little bit the energy DOES go to the higher harmonics, but the coupling is weak ...


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What you are suggesting is modeling a continuum object as an N-spring, M-point mass system. Such a system can be modeled in terms of a set of N 2nd order linear differential equations and further expressed as a linear state space system. In linear systems theory the observability and contollability of the the state space system can be determined and given ...



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