Two blocks are connected by a spring. The combination is suspended, at rest, from a string attatched to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, what is the initial downward acceleration of the upper block of mass 2m ?

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Before the string breaks: spring force on the lower block $F_{s} = m g$ ; tension in the string $T_{1} = 2 m g + F_{s} = 3 m g$ .

Just after the string breaks, $T_{1}$ becomes zero but the spring force stays $m g$ (the spring length cannot change instantly).

For the upper block $2 m$ : $2 m g + m g = 2 ma \Rightarrow a = \frac{3 g}{2}$ downward.

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