The points $$\(A\)$$ and $$\(B\)$$ are at the same horizontal level a distance $$\(4 a\)$$ apart. The ends of a light elastic string, of natural length $$\(4 a\)$$ and modulus of elasticity $$\(\lambda\)$$, are attached to $$\(A\)$$ and $$\(B\)$$. A particle $$\(P\)$$ of mass $$\(m\)$$ is attached to the midpoint of the string. The system is in equilibrium with $$\(P\)$$ at a distance $$\(\frac{3}{2} a\)$$ below $$\(M\)$$, the midpoint of $$\(A B\)$$. Find, in terms of $$\(a\)$$ and $$\(g\)$$, the speed of $$\(P\)$$ as it passes through $$\(M\)$$ in the subsequent motion. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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