Physics Demonstrations

We are creating a simple pendulum with a mass at the end of a massless string. Using both linear and non-linear solutions, we solve the second order differential equation $\stackrel{\mathrm{..}}{\theta }=\frac{-gsin\theta }{l}$ in state space. We use state space to set up our system of equations in order to use numerical integration methods like the Runge-Kutta Method. In this simulation, we use the ordinary differential equation libaray from SciPy for the nonlinear solution while the linear solution is ${\theta }_{o}cos\left(\omega t\right)$.

While the html form is my design, the solution code came from the YouTube Channel Good Vibrations with Freeball, specifically the video Coding a Numerical Solution to the Simple Pendulum Problem using Python. Download the base code from Freeball's GitHub.

Some questions to consider when viewing this demonstration:

• Compare the effects of length and angle on the period of oscillation (the time to return to the initial position).
• Analyze the phase differeneces (the differences in position for a specific time) betwen the linear and nonlinear for different angles, time steps.
• What everyday objects exhibit a pendulum behaivor?