Math IA Pendulum Graph

Graph plot and visualisation of percentage error between approximated time period formula used in IB Physics and exact time period, against initial angle of bob.

Files

• pendulum.cpp: C++ program that calculates the percentage error for different initial angles.
• plot_pendulum_data.py: Python script that reads the data generated by the C++ program and plots a graph.

Usage

C++ Program

Compile the C++ program:

g++ pendulum.cpp -o pendulum

Run the compiled program:

./pendulum

Python Script

Ensure you have the required Python packages installed:

pip3 install numpy matplotlib scipy

Run the Python script to plot the data and fit a quadratic curve:

python3 plot_pendulum_data.py

Results

The generated graph illustrates the relationship between the initial angle and the percentage error. A quadratic curve has been fitted to the data to capture the underlying trend.

Fitted Equation

The fitted equation for the quadratic curve is:

Fitted Equation

The fitted equation for the quadratic curve is:

$$ f(x) = 0.00246396 \cdot x^2 - 0.02765015 \cdot x + 0.22808328 $$

This equation can be used to predict the percentage error for a given initial angle.

Measurement Accuracy

For a good measurement system, the accuracy error should be within 5% and the precision error should be within 10%.