In this work we propose an inexpensive laboratory practice for the laboratory of an introductory course of Physics for any grade of Sciences and Engineering, which was very well received by our students, where a smartphone (iOS, Android or Windows Phone is irrelevant) is used together with some mini magnets, similar to those that can be found in the door of our refrigerators, a 20 cm long school rule, a paper and a free application (app) for measuring the magnetic field using the magnetic fields sensor or magnetometer of the smartphone, which needs to be downloaded and installed. The apps we have used are: Magnetometer (iOS), Magnetometer Metal Detector and Physics Toolbox Magnetometer (Android). Nothing else is needed. Cost of this practice: 0 coins. The main purpose of the practice is that students determine the dependence of the component x of the magnetic field produced by different magnets (from the typical magnets that are decorated in refrigerators even with a ring magnet and spherical magnet). We have obtained that the dependency of the magnetic field with the distance is of the form x -3 , in total agreement with the theoretical analysis. The secondary objective is to apply the technique of least squares fit to obtain this exponent and the magnetic moment of the magnets, with theirs corresponding absolute error.

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An approximate scheme for obtaining the period of a simple pendulum for large amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be done which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the KiddFogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.