Newton’s cradle

Last updated on Saturday, 27 July 2019
Download Mathematica notebook with this post.

Introduction

Here we are simulating Newton’ s cradle using springs and masses. Each mass is modelled by a number of smaller masses (here 10) with springs between them. We consider five groups of ten smaller masses, i.e. five masses with each group in an weak external harmonic potential corresponding to the pendulum effect for each mass.

Initialisation parameters

Setting up the spring matrices

In a first step we setup the spring interaction between each neighbouring small mass. The figure shows that there is no spring between each group of small masses.

Interaction between forces

The springs between groups are setup identically to the springs between the small masses. These interactions are only switched on when the distance between boundary small masses is smaller then the equilibrium length of a spring.

Defining equations, solving and plotting

Equations are setup together with the weak external potential.