Conservation of energy -- Two charges separated by a spring

[Roxas ross]

1. Two identical charged particles which are point masses are fastened to the two ends of a spring of spring constant 100 N/m and the natural length 10cm.The system rests on a smooth horizontal table.The charge of each particle is 2*10^(-8)C.the extension of spring if the extension is small as compared to the natural length.2. Coulomb's force =1/4πe* q^2/d^2
Sring energy= 0.5* k *x^2
Spring force=k*x
3. I used energy conservation theorem and since the final and initial velocities of the particles are 0 I obtained the extension which was twice the extension as compared to the answer i got by equating forces.the force method is given as the correct answer.what is wrong in my method?

 

[haruspex]

What exactly is the question? Is the word "find" missing? Anything else?

the extension of spring if the extension is small as compared to the natural length.

Not sure why the size condition is needed.

It is not clear whether the system starts with the spring at its natural length, and is then released, or perhaps it is lying in equilibrium. Energy will find the max extension in the first case, but is not helpful in the second.

 

[Roxas ross]

What exactly is the question? Is the word "find" missing? Anything else?

Not sure why the size condition is needed.

It is not clear whether the system starts with the spring at its natural length, and is then released, or perhaps it is lying in equilibrium. Energy will find the max extension in the first case, but is not helpful in the second.

The question asked is to find the extension in the spring .thThe size condition is needed because if the extension of the spring is not small in common to it natural length then the coulombic force will change at significantly at every instant during the elongation process.The system starts with the spring at its natural length, and is then released

 

[haruspex]

The question asked is to find the extension in the spring .thThe size condition is needed because if the extension of the spring is not small in common to it natural length then the coulombic force will change at significantly at every instant during the elongation process.The system starts with the spring at its natural length, and is then released

Ok.
Assuming it is asking for the maximum extension, that would indeed be twice the equilibrium extension (which I assume is what you found by the force method).
As a check, please post your detailed working for the force method.

 

[mfb]

If you start with the system at the natural extension, it will oscillate around the equilibrium position forever. What you calculated with conservation of energy are the two endpoints of this oscillation. The force balance gives the equilibrium position.