### The Pendulum Catch

#### (supervisor: Adil Mughal)

Nature of project: **experimental**, theory

Available to
students on full-time physics degree schemes or joint students.

#### Project description and methodology

The pendulum catch is a poorly understood phenomena whereby a falling pendulum becomes ensured by its own tail. A video of this phenomena in action can be found here:

https://www.stevespanglerscience.com/lab/experiments/magic-pendulum/

In this project you will first construct an experimental apparatus for demonstrating the pendulum catch. To take this project further you will film the process using a high speed camera.

*A successful project will develop beyond the above in one/some of the following directions:*

To advance the project beyond the basic level you will write down the equations of motion for a falling pendulum. The resulting coupled second order differential equations can then be solved numerically to produce a phase diagram that plots the variables for which the pendulum is caught.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

*Additional scope or challenge if taken as a Year-4 project:* Compare numerical results against experiments. Develop a simple theory for the pendulum catch for some ideal values of the starting configuration.

Please speak to **Adil Mughal** if you consider doing this project.

*Initial literature for students:*

- https://www.stevespanglerscience.com/lab/experiments/magic-pendulum/
- Wells DA. Schaum's outline of theory and problems of Lagrangian dynamics: with a treatment of Euler's equations of motion, Hamilton's equations and Hamilton's principle. McGraw-Hill; 1967.
- Morin D. Introduction to classical mechanics: with problems and solutions. Cambridge University Press; 2008 Jan 10.

#### Novelty, degree of difficulty and amount of assistance required

Assistance and training required to use the high speed camera. Some small amount of technical support to build the experiment.

#### Project milestones and deliverables (including timescale)

milestone | to be completed by |

Build and run the experiment | end of November |

Numerical solution of differential equations | Christmas |

Compare experiments with numerics | end of February |

Write up report + theory | Easter |

Students taking this project will have to submit a full *risk assessment* form