Introduction to the Fourier transform studying the oscillations of a pendulum

Students of physics, engineering and related majors; generally, do not know the usefulness and applications of transforming a signal from the time domain to the frequency domain. The mathematics that makes possible this transformation is well known to senior students of the majors, but vaguely applied in teaching laboratories. The main phenomena that could provide us with frequency information, the pendulum and the spring, are minimized by focusing only on obtaining the mathematics dictated in books.  The pendulum is the most studied physical system in teaching laboratories from precollege up to college levels; this phenomenon is analyzed mathematically in most of the related literature in the area of Physics and Engineering. It is an introduction to the wave phenomenon. However, teaching paradigms, focus on the plain demonstration that periods are invariant to suspended masses, if and only if the oscillation is within angles not greater than 10 degrees from their normal. The use of technologies, computational and electronic, also focuses on the demonstration of such assertion. In the present work, a mechanical-electrical system was designed that allows to observe, in real time, on the screen of an oscilloscope, the swinging behavior of a pendulum. This system makes evident that the swing movement of a pendulum can be described by a sine function, but also with this same system, and with the help of a digital oscilloscope, it is possible to simultaneously observe the signal generated in the temporal domain and in the frequency domain. This innovation not just breaks the paradigms of teaching but also promotes an alternative to valuable observations promotes understanding.