I'm adding a link to a folder that contains the after effects file and the source image so if you have After Effects you can open the file and see how it works - or make modifications if you want.
• Source: ???
Link to folder: mega.nz folder I'll need to make a page here explaining the expression I used, but basically you give it three keyframes: start, sling, and end. The middle keyframe (sling) controls how fast and how far the sling/bounce happens. It works pretty well consider it has so few options. If you open the .aep file, the expression is in the Assemble comp, on the LEFT CHEST layer, under the "horiz" and "vert" effects. I also made a little test zone in a comp for people to just play with.