Matplotlib-Visualizations

To simulate a pendulum in Python, you can use various libraries such as matplotlib for visualization and numpy for numerical computations. Below is an example of how to simulate a simple pendulum using the Euler method for numerical integration.

Step 1: Install Required Libraries

First, make sure you have the necessary libraries installed. You can install them using pip:

pip install numpy matplotlib

Step 2: Write the Pendulum Simulation Code in this File (Simulation Code.py)

Explanation:

• Parameters:

• g is the acceleration due to gravity.
• L is the length of the pendulum.
• theta0 is the initial angle of the pendulum.
• omega0 is the initial angular velocity.
• t_max is the maximum time for the simulation.
• dt is the time step for the Euler method.

Euler Method:

• The angular acceleration alpha is calculated using the pendulum equation: α = − g L sin ⁡ ( θ ) α=− L g ​ sin(θ).
• The angular velocity omega and angle theta are updated using the Euler method:
• ω = ω + α ⋅ d t ω=ω+α⋅dt
• θ = θ + ω ⋅ d t θ=θ+ω⋅dt

Plotting:

The angle and angular velocity are plotted against time.

Step 3: Run the Code

Run the code in your Python environment. You should see two plots: one showing the angle of the pendulum over time, and the other showing the angular velocity over time.

Notes:

The Euler method is simple but not the most accurate for long simulations. For better accuracy, consider using more advanced numerical methods like the Runge-Kutta method.

The simulation assumes a small damping factor (none in this case), which is why the pendulum oscillates indefinitely. In reality, air resistance and friction would cause the pendulum to slow down over time.