(A level Phy) Deriving the period for a glass moving on a rotating table

What are everyday examples of Simple Harmonic Motion? 

I remember once my A Level Physics tutor was absent. Another tutor came into the class or more precisely the Physics laboratory. I don't like the baking air of the laboratory, making the afternoon tutorial unbearably drowsy. With the monotonous and muffled voice of my original Physics tutor, the battle with the Z-monster was almost impossible. But being much more commanding than our original tutor, this relief tutor effectively exorcised the Z-monster in me. There's no introduction needed as we'd frequently seen this other tutor in lectures on many topics such as Mechanics and Modern Physics. He didn't need to know us too, and so without any delay, he demanded an everyday example of the Simple Harmonic Motion together with its application from each of us. No one is to cite an example that's previously been used by another student. In such a case, I rather be one of the first to be asked. Unfortunately, my turn was the last. The simple pendulum, the high and low tide, the bungee jump, the diving board, musical instruments, earthquakes etc. I'd run out of examples. I had no choice but to say something which does not have an application. I said “A glass of Chinese tea placed on a rotating round table.” He asked, “Where's the SHM?” I replied, “If you shine a light from the side, you see the shadow of the glass going to and fro. This is SHM.” Luckily, he is satisfied. There didn't seem to be any application for this and so he proceeded to the SHM tutorial questions.

The shadow of a glass moving around on a rotating table makes an SHM… 

Let's derive the expression for the period T in the example of the orbiting glass of Chinese tea. There are two ways of doing this. Both use classical Newtonian mechanics. But one is by the Circular Motion and the other is by the Simple Harmonic Motion. 




Actually, they're of the same method, aren't they? They both make use of the result of Newton's Second Law F = ma where a = v2/r = (2πr/T)2/r = (2π/T)2 (r2/r) = rω2. The second way, however, begins with the solution of SHM, r = ro sin ωt which still leads to a = -rω2. 

For Circular Motion, we use a = rω2… For SHM, we use a = -rω2... 

We've seen how the period of the glass of Chinese tea moving in a circular motion or how its shadow moving in SHM is derived. But what use can the SHM from a glass of Chinese tea on a rotating table have?