I would imagine if you placed a half full water bottle on the floor of the car you can see the vibration transferred to the water. If you placed the bottle on the top of your sling I'm betting you will see is as well.
For science, I recommend placing the bottle on the equipment at different points (motor, gear box, brake, machine beam, you could even tape it to the ropes). It's not sophisticated but it is effective.
I'm leaning toward the machine vibration transferring through the ropes. If it is I would check the motor alignment, thrust, brake & and root clearance.
Let us know how you make out...
