Our second semester of the year started on Monday, and I have begun teaching a course on dynamics of machines, for the first time. (That is, it’s the first time I have taught it). Although I’m familiar with a lot of the material, there are bits of the course that are new to me, as well as my students, which I am finding very interesting (the new bits of the course, not the students). I’ll relate one of these to you.
Imagine you have built a small tower in your garden – maybe a tree house for your kids, maybe a structure to put a satellite dish on – it doesn’t matter, but it is a structure that will be loaded – that is, a big weight will be placed on it. Now, the question you want answered is how much weight will your structure be able to support before it collapses?
There is an easy way to find out. Keep loading it up until it collapses. That will tell you the answer, but it has the minor drawback of destroying your tower. How can you tell without destroying it in the process?
One method is to study the way the tower wobbles when it is pushed slightly. Every structure has its own natural frequencies of vibration (the number of wobbles it does every second), and these depend on the loading of the structure. A very useful piece of physics tells us that the frequency of wobbling decreases as a tower is loaded, and just at the point of collapse, the frequency of wobbling is zero – that is, a small push is never rectified. Which means that all you need do is to measure the frequency of wobble as you load up the structure, and when the wobble frequency gets close to zero, you know you are getting close to collapse.
You can hear the same effect with a guitar string. When properly tensioned, the string gives its correct pitch when plucked. Now, decrease the tension on the string (which is like loading the tower) and the pitch of the string drops. Keep decreasing it, and there comes a point where its oscillations are so slow that you can barely hear it. Just beyond this point, the string will buckle; this is equivalent to the tower collapsing. That is, you can tell when the string is about to buckle just by listening to it. Likewise with structures. Very useful.