Modeling a pendulum

Jonathon Sumner
Physics Department
Dawson College
Jean-François Brière
Physics Department
Dawson College
Sameer Bhatnagar
Physics Department
Dawson College
March 4, 2019
March 12, 2019

Meeting 3

Studying the behaviour of a pendulum beyond the small angle approximation by using numerical methods

Lecture notes

This lecture will first revisit a classic from your Waves course: the pendulum. However, we will see how numerical methods can be used to study the pendulum beyond the small angle approximations.

From the pendulum to chaos
Intro to numerical methods for ODEs

Pre-lab

Write the pseudocode to solve the equation of motion of the pendulum using Verlet's method.

Due at the beginning of the lab.

To give you an idea, the generic pseudocode of Euler's method we saw in class is shown below. We want something equivalent that will show how to apply Verlet's method to the pendulum.

Set initial conditions x[0], t[0]

Set end time tFinal

Set step size dt

Start loop

x[i+1] = x[i] + f(x[i],t[i]) * dt

t[i+1] = t[i] + dt

Continue while t[i+1] < tFinal