Here is a link to my first physics scratch project:
This project is the equation of motion for a pendulum where you can enter the mass and angle where it is released. It also tells you the kinetic and potential energy.
I had to derive the formula for the equation of motion of a pendulum using the euler-lagrange equation from classical mechanics which uses the principle of least action to find equations of motion. After that I had to turn this equation of motion into an actual animation on the computer screen.