Re: a “vibrating” saw
Probably one of these:
https://fein.com/en_uk/oscillating-multi-tool/multimaster/fein-multimaster-fmm-350-qsl-edition-2017-0372811/
Very useful for awkward jobs and safe to use close to the human body as the blades don't grab (I think they're also used for removing plaster casts). Still, I prefer to keep mine away from my body parts. (So far I've only worried about my fingers, but now ....)
Though it looks like they broke the cast iron (relatively brittle) weight rather than cutting all the way through it.