Harmonious Spring Pendulum (xyz) Mechanics Analyze the frequency and period of a spring oscillator and display the elogation of the pendulum. This experiment uses the accelerometer to measure the oscillator movement and calculates the oscillation period T. Using the circular frequency it transfers the data of the accelerometer into the elogation. Further details: The oscillation period is obtained through the autocorrelation of each accelerometer 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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 Harmonisches Federpendel (xyz) Mechanik Misst die Frequenz und Periode eines Federpendels und zeigt die Auslenkung des Pendels an. Dieses Experiment nutzt den Beschleunigungssensor um die Pendelbewegung zu erfassen und berechnet hieraus die Schwingungsperiode T. Mit Hilfe der Kreisfrequenz wird aus den Beschleunigungsdaten die Elogation bestimmt. Weitere Details: Die Schwingungsperiode wird durch eine Autokorrelation jeder Komponente des Beschleunigungs-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. Elongation (x-Achse des Smartphones) Elongation (y-Achse des Smartphones) Elongation (z-Achse des Smartphones) Ergebnisse Periode Frequenz Kreisfrequenz Federkonstante Masse Federkonstante Rohdaten Beschleunigung X Beschleunigung Y Beschleunigung Z accX accY accZ acc_time autocorrelation_x autocorrelation_y autocorrelation_z autocorrelation_t autocorrelation dt t0 t1 t2 search_t search_y period frequency autocorrelation_t (1) autocorrelation_t (2) circular frequency omega2 eloX ampX ampX (1) eloY eloZ mass product power spring constant eloXcm eloYcm eloZcm accX accY accZ acc_time acc_time accX 0 2.5 autocorrelation_t autocorrelation_x acc_time accY 0 2.5 autocorrelation_t (1) autocorrelation_y acc_time accZ 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 frequency 6.2832 circular frequency circular frequency 2 omega2 accX omega2 -1 eloX 100 eloX eloXcm accY omega2 -1 eloY 100 eloY eloYcm accZ omega2 -1 eloZ 100 eloZ eloZcm mass 39.4784 product period 2 power product power spring constant eloXcm acc_time eloYcm acc_time eloZcm acc_time period frequency circular frequency mass spring constant accX acc_time accY acc_time accZ acc_time acc_time eloXcm eloYcm eloZcm period frequency spring constant acc_time accX accY accZ