Finding the max. extension in the spring

AI Thread Summary
To find the maximum extension in a spring attached to two blocks of masses m and M, the system is analyzed on a smooth surface with an external force F acting on mass M. The original solution uses the center of mass (COM) reference frame and incorporates pseudo forces, which some find tedious. A request is made for a simpler alternative approach to solve the problem. The result from the original solution is sought for comparison with any new methods proposed. A clear and straightforward solution is desired to enhance understanding of the spring's behavior in this setup.
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finding the max. extension in the spring...!

Okkay so i have to calculate the max. extension in a spring attached with two blocks of mass m and M. The box of mass M is pulled with a force F. The system (blocks of masses m1 and m2 and the mass less spring) is placed on a smooth surface.

Actually the soln. given is quite boring.. they have used the reference frame of the system.. taking the COM (center of mass) of the system as the origin and the acceleration of COM is taken and all that... and most importantly psudo force is applied...

now what i want is.. a good and easy soln. to it... if someone could help... !
 
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What was the result of the boring solution? Useful for comparing with an alternate solution.
 

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