Gravitational Collapse of a Spherical Shell?

A while ago at high school, I was once walking down the hallway when I noticed my beloved physics teacher heading towards me wearing a big smile on his face. I knew what was coming, another one of his classic “try to solve this problem, if you can” moments. However, the level of his excitement […]

An Introduction to Calculus of Variations

What is Calculus of Variations? In general, developments in mathematics are motivated by the need for them in applications. Calculus of variations is no exception. In fact, it was first developed in 1969 when Johann Bernoulli asked the greatest mathematical minds of his time to solve the famous ‘brachistochrone problem’. This problem involves a bead […]

Can a wave be represented by infinite discrete oscillators?

In this article I will find the equation of motion for an arbitrary number of discrete coupled oscillators (I will call “beads”) on a string. Then we will take the limit as the number of oscillators tends towards infinity, and see if the wave equation can be reproduced. If so it would be a good […]