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A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals a third the kinetic energy?

I have attempted this problem many times incorrectly. The answers I have inputted have been A/sqrt2, sqrt2, A sqrt( 1/2), A12, 1/sqrt2, .707. Apparently the correct answer does not depend on A in the solution because A is already listed in d= (answer) A. Please help and don't answer with any of the above previously incorrectly used solutions.

My professor helped me get this far and he says this is a few steps away from the final answer. Just need to simplify but I have no idea how.

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