pendulum_motion

Simple Pendulum

This project started with me wanting to code for pendulum waves.

Important reads:

• The Simple Pendulum (Pennsylvania State University) I found this page while surfing and its amazing. I ended up recreatig all of its animations.
• Pendulum wave (Wikipedia)
• Runge-Kutta methods (Wikipedia)

Equations

• Differential equation
  • $\frac{d^{2}\theta}{dt^{2}} + \frac{g}{L}sin(\theta) = 0$
• Converting it into two first order equations
  • $\frac{d\theta}{dt}=\omega$
  • $\frac{d\omega}{dt}=-\frac{g}{L}sin(\theta)$
• Small angle approximation
  • $sin(\theta) \approxeq \theta$

Output

Execution work product of pendulum_waves.py module.

Linear ordinary differential equations (ODEs) are solved for $\theta = 10 \degree$.

pendulum_waves.mp4

Execution work product of linear_pendulum_motion.py module.

This compares and captures the proportionality of time period of simple pendulum on string length. Again, linear ordinary differential equations (ODEs) are solved for $\theta = 10 \degree$

pendulum_motion.varying_string_length.mp4

Execution work product of linear_and_non_linear_pendulum_motion.py module.

This captures the effect of approximation of $sin(\theta) \approxeq \theta$ for small angles. Notice that for $\theta = 10 \degree$ approximation provides acceptable results.

linear_and_non_linear_simple_pendulum.mp4