Hi,
Welcome to the forum from me too Alex.
First because school and bandsaw are mentioned are you aware of the safety rules/regulations involved?
https://www.machinesafety.co.uk/news/safeguarding-machinery-in-schools-and-colleges/
With that out of the way back to your question; I fully agree with Doug regarding the weight of the motor being often used for tensioning the drive belt; am I correct you're located in the UK given the bandsaw is a 352 and is it a Startrite? If it is a Startrite then it's a nice bandsaw. I used to own a Startrite Volant 24" ten speed with band cutter and welder onboard.
My Startrite had it's motor on an hinged base with a strong spring to prevent the motor suddenly jumping upwards so yes the motor did feel loose but of course the motor mounting plate still requires to be securely attached to the saw body easily checked by checking the securing points.
If the saw is an old model then it could well fail modern safety standards as to motor braking and guarding also any electrical work is covered by strict regulations requiring being carried out be a competent person? Sorry if I sound negative but a lost finger could prove costly indeed.
Kind regards, Colin.
View attachment 1816
My Startrite Volant 24" nearing full restoration.
View attachment 1817
This Startrite is a big industrial bandsaw on 3 phase 415V and I was running it through my own huge transformer powering it on 415V but from our domestic 240V supply; these are the capacitors used to phase balance the motor to the transformer; the transformer wasn't a static converter it was a purpose built transformer wound by me and it behaved just as if 3 phase 415V supply was laid into the workshop. Much too complicated and dangerous to fully discuss here; I've since sold my big 3 phase machinery and the transformer is now with an electrical engineer so I know its in safe hands.