What is a creative way to display a family tree?

What is a practical way to determine the natural oscillatory frequencies of individual, successively smaller branches of a natural form like a tree?

• This is inspired by looking at how a flowering tree outside my window moves in a breeze.  The flowers, sitting on the smallest branches of the tree, act like springs in the wind, moving back and forth with definite periodicity.  Many of these flowering branches connect to a single larger branch, which itself moves with slower periodicity.  I can imagine that the whole tree, in a breeze, is like a symphony of various overtones far below the threshold of human hearing.  I can imagine that each individual species tends towards some basic set of oscillations: each tree has its own "music".  I can further imagine that having this data for a given tree, one could multiply the frequency by some appropriate constant that would put the frequencies into the human range, and allow one to audibly construct the music of the tree with a suitable program. Is this a case where one would have to use the universal oscillator equation to model the behavior, or can more simple mathematics be used?

• Answer:

  In general, you need to apply an alternating force that you can vary the frequency of (or a random force that spans frequencies of interest), then monitor the displacement and look for a peak at a particular frequency that is the resonance. There are lots of different types of forcers, and lots of different types of sensors, and you'll need something like an oscilloscope, or even better if you can wrangle one, a spectrum analyzer. But something about the way you phrase the question makes me worry that you don't understand exactly what you're trying to measure. Note that individual branches don't have separate frequencies in the context of the whole tree - any resonances are the property of the tree as a whole. Of course you can make a branch into a whole system, by clamping it at its base and thereby isolating it, but how it oscillates in that state may be very different from how it would oscillate as part of the whole tree.