See the Cylinder below. This is unbalance at two point at both ends. And it need to be balanced at both ends for both the heavy spots.this is a two plane balancing.it can be done only dynamically.
Now lets imagine (I hope you can) its thickness is very low or in other words compress this to near zero thickness. Practically both the unbalances are on same plane and you can find out a single point to put counterweight for balancing. And thats a single plane balancing.you can do its statically and dynamically.
Also check the earlier post on static and dynamic balancing (the static is as single plane balancing)
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