Honestly, sometimes I wonder if we overthink this stuff lol. Like @umabailey's example is cool and all, but most people just want to hear "it's old and needs a fix" not a whole science fair project. If the elevator shudders, they already know something's wrong, the why is just extra. Maybe we make it more serious than it needs to be.
I read a blog post once that said explaining counterweights is like trying to describe why a door doesn't close right. You can talk about pivot points and how weight is spread, but most people just want to know why their elevator shudders. I saw a video where a mechanic used a water bottle and a book to show how imbalance causes strain. The owner finally got it when he saw the bottle tip over. Stuff like that makes more sense than talking about torque or wear on parts. Idk, maybe it's just me, but it's all about finding a simple way to show the problem.