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Learn Challenge: Visualize Pendulum Data | Data Analysis and Visualization in Physics
Python for Physics Students

bookChallenge: Visualize Pendulum Data

You are given time and angle data collected from a pendulum experiment. Your task is to analyze this data by visualizing the pendulum's oscillations and determining the period of its motion. This exercise will help you practice working with real experimental data, plotting time series, and extracting physical parameters such as the period from oscillatory motion.

Task

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You are given arrays of time and angle data from a pendulum experiment. Your task is to write a function that analyzes this data to determine the period of the pendulum's oscillation and visualize its motion.

Follow these steps:

  • Define a function that takes two arguments: a time array and an angle array, both of the same length.
  • Plot the angle as a function of time using matplotlib to visualize the pendulum's oscillations. The plot must include:
    • A labeled x-axis ('Time (s)') and y-axis ('Angle (degrees)').
    • A title (such as 'Pendulum Oscillation').
    • A legend indicating the plotted data.
  • Use scipy.signal.find_peaks to detect the local maxima (peaks) in the angle data. These peaks correspond to the times when the pendulum reaches its maximum displacement in each oscillation.
  • Determine the times corresponding to these detected peaks.
  • Calculate the differences between successive peak times to estimate the period of each oscillation.
  • Compute the average of these periods to obtain the pendulum's overall period.
  • If fewer than two peaks are detected (i.e., it is not possible to compute a period), your function should return None.
  • Print the computed period (or None if not enough peaks are found) and return it as a float value (or None).

This function will help you practice extracting physical parameters from experimental data and visualizing oscillatory motion. Accurate peak detection is essential for reliable period estimation.

Solution

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SectionΒ 3. ChapterΒ 3
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bookChallenge: Visualize Pendulum Data

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You are given time and angle data collected from a pendulum experiment. Your task is to analyze this data by visualizing the pendulum's oscillations and determining the period of its motion. This exercise will help you practice working with real experimental data, plotting time series, and extracting physical parameters such as the period from oscillatory motion.

Task

Swipe to start coding

You are given arrays of time and angle data from a pendulum experiment. Your task is to write a function that analyzes this data to determine the period of the pendulum's oscillation and visualize its motion.

Follow these steps:

  • Define a function that takes two arguments: a time array and an angle array, both of the same length.
  • Plot the angle as a function of time using matplotlib to visualize the pendulum's oscillations. The plot must include:
    • A labeled x-axis ('Time (s)') and y-axis ('Angle (degrees)').
    • A title (such as 'Pendulum Oscillation').
    • A legend indicating the plotted data.
  • Use scipy.signal.find_peaks to detect the local maxima (peaks) in the angle data. These peaks correspond to the times when the pendulum reaches its maximum displacement in each oscillation.
  • Determine the times corresponding to these detected peaks.
  • Calculate the differences between successive peak times to estimate the period of each oscillation.
  • Compute the average of these periods to obtain the pendulum's overall period.
  • If fewer than two peaks are detected (i.e., it is not possible to compute a period), your function should return None.
  • Print the computed period (or None if not enough peaks are found) and return it as a float value (or None).

This function will help you practice extracting physical parameters from experimental data and visualizing oscillatory motion. Accurate peak detection is essential for reliable period estimation.

Solution

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SectionΒ 3. ChapterΒ 3
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