Please explain with strings....
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Here is the solution.
The question is having a spring, so I don't know how to explain it with 'string' but I can try.
You can think of the spring as a string which pulls both blocks towards its center with a force of 'kx.' In case of string, it would pull both with force 'T' (for tension) towards its center.
Consequently, you can replace 'kx' in the above solution with 'T' and reach the same solution, but it would make little sense, since when attached by a string in same case, both blocks will have same the acceleration instead of dissimilar values for it.
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