A small ball of mass M is attached to two identical springs of constant k, which are attached to floor and roof. The springs have unstretched length $l /2$ . At what distance from the ceiling ball remain at equilibrium?

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Let the ball be at distance x from the ceiling. Upper spring extension = x − 2 l ​ ; lower spring extension = 2 l ​ − x . Equilibrium: k ( x − 2 l ​ ) = M g + k ( 2 l ​ − x ) . 2 k ( x − 2 l ​ ) = M g ⇒ x = 2 l ​ ( 1 + k l M g ​ ) .

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