In this work the contents of an academic lecture addressed to first year
Physics students on a system of coupled oscillators is presented. More specifically, the
physical system dealt is constituted by two oscillating masses interacting through a
connecting spring. At first, the theory describing the system dynamics is presented by
putting into evidence how the diagonalization process allows to reduce the coupled
oscillation equations to formally simpler, but physically equivalent, expressions which
make reference to uncoupled oscillations and how the new chosen coordinates do not
refer to the positions of the real masses but describe collective properties of the system,
namely its normal modes. To facilitate the comprehension of the analytical procedure,
an experiment addressed to characterize the system normal mode frequencies is
proposed. On this purpose, for analysing the oscillation amplitude as a function of time,
a comparison between Fourier Transform and Wavelet Transform is presented. What it
emerges is that, differently from what occurs for Fourier Transform which provides a
value of the motion average frequency, the Wavelet Transform allows to
simultaneously execute a time–frequency analysis.
Keywords: Coupled oscillators, Fourier Transform, Wavelet Transform.
