Infinite Atwood’s machine

The infinite Atwood’s machine shown has a string passing over each pulley, with one end attached to a mass and the other end attached to another pulley.

The masses are held fixed and then released simultaneously, and the acceleration of the top mass is \(\lambda g.\)

What is \(\lambda?\)

Details and Assumptions:

  • All the masses are equal to \(M\).
  • All the pulleys and strings are massless.
  • \(g\) is the acceleration due to gravity.
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