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## Homework Statement

F <-- M------------------------------------M →F

Two equal masses M are connected by a spring having spring constant k, as shown above.

We have to find the maximum elongation of the spring if two equal forces F are applied in opposite directions..

## Homework Equations

Please, there are many equations.

## The Attempt at a Solution

I solved it via two methods and those two give different answers.

Due to symmetry the centre of mass will be at mid point and let elongation at either side be x, Now the spring constant of each half will be 2k.

First method: Work done by the forces on a system = Change in kinetic energy + Change in potential energy of the system :

2Fx = 0 + 2(2kx

^{2})/2

thus x = F/k

Therefore total elongation = 2x = 2F/k

Method II :

F = 2kx

or x = F/2k

Total elongation = 2x = F/k

Which answer is wrong ?

Please help !!