Problem: A non-uniform beam with a mass 3 M and length L is in stable equilibrium when placed at the edge of a table with half its length sticking off the table edge. But when a pointlike mass M is placed at the far end of the part of the beam off the table, the beam is brought to unstable equilibrium; i.e., it is right on the verge of tipping off the table.  At what distance to the left of the table edge is the center of mass of the beam located?

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A non-uniform beam with a mass 3 M and length L is in stable equilibrium when placed at the edge of a table with half its length sticking off the table edge. But when a pointlike mass M is placed at the far end of the part of the beam off the table, the beam is brought to unstable equilibrium; i.e., it is right on the verge of tipping off the table. 

At what distance to the left of the table edge is the center of mass of the beam located?