What might be an example of the use of the Heisenberg Uncertainty Principles use outside of quantum mechanics?
Outside of QM, relations like the HUP are not usually given that name, but do exist, wherever wave descriptions (and Fourier analysis) apply. For instance, for sound waves (or any other waves for that matter), a wavepacket which is sharp in time (like a thunderclap, localized in the “time domain”) is composed of a superposition of sound waves very spread out in frequency. A pure frequency tone (localized in the “frequency domain”) is spread out in time.