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I came across a problem as below :

2 masses M1 and M2 are connected by a spring and kept on a frictionless table horizontally. A force F is applied to M2. What is the maximum displacement of the spring ?

The acc of the COM of the system is a = F/(m1 + m2).

However, each mass will move with different acceleration because of the spring between them. If x1 and x2 are the displacements at M1 and M2, the force exerted by the spring on each mass will be k(x1-x2).

FBD of M1 gives

k(x1-x2) = M1 a1

FBD of M2 gives

F-k(x1-x2) = M2 a2

I'm not clear how to proceed from here. The ans is

2M1 * F / (M1 + M2)

Cany anypone explain ?

TIA

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# How to find max deflection of spring between 2 masses ?

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