59 posts on physics. All posts · RSS feed
The previous blog post described the normal modes of a chain swinging under its own weight. Here we describe the motion of a chain after an arbitrary displacement as a linear combination of such normal modes. The code for this project is on my github …
The description of the oscillations of a hanging chain was a problem in mechanics solved by Daniel Bernoulli in the 18th century and which led to the discovery of the class of functions known as Bessel functions. The code for this article is hosted on …
This post is based on Problem 2.22 from Griffiths, Introduction to Quantum Mechanics (Prentice Hall, 1995). A free particle prepared in the initial state (where is a constant) evolves according to the Schrödinger equation as From , the probability distribution function can be shown to …
For the purposes of this article, the harmonically-driven pendulum is one whose anchor point moves in time according to . As with previous posts, the position of the pendulum bob with time can be described using Lagrangian mechanics. In a coordinate system with the pendulum …
Following on from the previous post on the double pendulum, here is a similar Python script for plotting the behaviour of the "spring pendulum": a bob of mass suspended from a fixed anchor by a massless spring. As before, the code places frames of the …
In classical mechanics, a double pendulum is a pendulum attached to the end of another pendulum. Its equations of motion are often written using the Lagrangian formulation of mechanics and solved numerically, which is the approach taken here. The dynamics of the double pendulum are …
A very simple diffusion simulation can be constructed in two dimensions by following the positions of a number of "particles" which all start off at the centre of a grid of cells. Time is assumed to progress in a series of "ticks": at each tick, …
The Brachistochrone problem asks the question "what is the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip, without friction, from one fixed point, to another in the least time?" Its solution is well-known and given in …
The temperature-dependence of the rotational contribution to the heat capacity of gaseous molecular hydrogen shows a Schottky anomaly: whereas for many systems the heat capacity can be expected to increase with increasing temperature, for there is an temperature range within which it reaches a maximum …
It is a standard result of statistical thermodynamics that the molar heat capacity at constant volume, , is related to the molecular partition sum, , through the relation where and represent the first and second derivative of with respect to the "thermodynamic beta", : There …
