枥 lives in one famous line by 曹操: 老骥伏枥，志在千里 ('the aged steed in its stall still longs to gallop a thousand miles'): an old person with great ambitions still.
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Literary and archaic; the 'oak' sense in particular appears only in classical texts.
木 is the wood radical, here in left-side form. A feeding trough is built of wood, and the character's other sense is a kind of oak, so the wood link works both ways.
