Swing (y) Mechanics Determine the period, frequency, and angle by using your phone as a swing. This experiment uses the gyroscope to measure the pendulum movement and calculates the oscillation period T. The user has to enter the length L of the string used for the pendulum, so phyphox can calculate the overall hight and the elongation of the pendulum. Further details: The oscillation period is obtained through the autocorrelation of each gyroscope component. The sum of three autocorrelations is then analyzed for its first maximum. As an autocorrelation shows a maximum at dt = 0, we look for the first time t0 it crosses zero. From there we expect the autocorrelation to oscillate as the pendulum gives a sine function. Through this assumption we extract the position of the first full maximum to be in the range 3 t0 to 5 t0 in which we look for the maximum value. 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 Schaukel (y) Mechanik Misst die Periodendauer, die Frequenz und die Winkelauslenkung indem das Smartphone als Schaukel benutzt wird. Dieses Experiment nutzt das Gyroskop um die Pendelbewegung zu erfassen und berechnet hieraus die Schwingungsperiode T. Der Nutzer muss die Länge des Pendels eingeben, so dass phyphox die Höhe und die Elongation berechnen kann. Weitere Details: Die Schwingungsperiode wird durch eine Autokorrelation jeder Komponente des Gyroskop-Vektors ermittelt. In der Summe aller drei Autokorrelationen wird dann nach dem ersten Maximum nach dem für Autokorrelationen üblichen Maximum bei dt = 0 gesucht. Hierzu wird der erste Zeitpunkt t0 ermittelt, bei welchem das Signal unter Null fällt. Unter der Annahme, dass die Autokorrelation periodisch um Null schwingt, wird das Maximum dann im Intervall 3x t0 bis 5x t0 gesucht. Eingabe Länge Masse Winkelauslenkung Winkelauslenkung Winkel (°) Ergebnisse Periode Frequenz Erdbeschleunigung g Rohdaten Gyroskop X Gyroskop Y Gyroskop Z gyr_time gyrX gyrY gyrZ length autocorrelation_x autocorrelation_y autocorrelation_z autocorrelation_t autocorrelation dt t0 t1 t2 search_t search_y period frequency pi2f g autocorrelation_t (1) autocorrelation_t (2) length (1) mass time differentiate angle differentiate_y offset angle_y max min abs abs (1) sum center angle_y offset_y angle_y degree_y gyrX gyrY gyrZ gyr_time gyr_time gyrX 0 2.5 autocorrelation_t autocorrelation_x gyr_time gyrY 0 2.5 autocorrelation_t (1) autocorrelation_y gyr_time gyrZ 0 2.5 autocorrelation_t (2) autocorrelation_z autocorrelation_x autocorrelation_y autocorrelation_z autocorrelation autocorrelation_t (2) autocorrelation t0 t0 2 dt t0 dt t1 t1 dt t2 autocorrelation_t (2) t1 t2 autocorrelation search_t search_y search_t search_y period 1 period frequency 6.283185307 frequency pi2f pi2f pi2f length (1) g gyr_time time differentiate time differentiate gyrY angle differentiate_y angle differentiate_y offset angle_y offset angle_y max offset angle_y min max abs min abs (1) abs abs (1) sum sum 2 center angle_y max center angle_y offset_y offset angle_y offset_y angle_y angle_y 57.2958 degree_y length (1) mass degree_y gyr_time period frequency g gyrX gyr_time gyrY gyr_time gyrZ gyr_time gyr_time degree_y gyr_time gyrX gyrY gyrZ period frequency g