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rsaad
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Hi! I have attached the picture. Can someone please tell me what equation of motion will be?
My guess is that it will be

[itex]\ddot{x}[/itex] = -k/x -kx/2
 

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What is x? What is "O"? What is fixed, what is not?
Those things labelled "k" are springs?
I don't think your answer is correct.
 
I think the signs are right, but it depends on the (unknown) original problem. However, an x in the denominator looks odd and I would expect to see a mass in the equation.