Variable length pendulum analyzed by a comparative Fourier and wavelet approach

The motion of a pendulum with a variable length is analyzed by means of a comparative Fourier and Wavelet approach. In particular Fourier and continuous Wavelet transforms have been jointly employed to investigate the non stationary signal of a variable length pendulum in an easy-to-interpret scenario addressed to undergraduate and graduate students. The comparison between the two data analysis protocols allows to easily show that while the Fourier transform is able to extract only an average frequency value for the variable length pendulum motion, Wavelet analysis furnishes information on the time behaviour of the motion spectral content, i.e. provides a joint time-frequency analysis.