How to Mitigate Sloshing

Walking across a room carrying a mug of coffee can often lead to spillage. Everyday experience tells us that it is better to walk slowly or not have the mug too full, but it is also well known that carrying coffee in a bucket with a pivoted handle is much less dangerous. Here we show how to construct a mathematical model for sloshing in the very similar problem of a mug on a smooth horizontal table forced to oscillate in one dimension via a spring connection. We find that analyzing this problem using quite simple ideas of mathematical modeling and analysis gives good physical understanding of how to reduce everyday sloshing.