When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $$\frac{x}{8}$$, where $$x =$$ _______.

Correct Answer: 9

Total energy = $$\frac{1}{2}kA^2$$. KE = $$\frac{1}{2}k(A^2 - x^2)$$.

$$\frac{E}{KE} = \frac{A^2}{A^2-x^2} = \frac{A^2}{A^2 - A^2/9} = \frac{1}{8/9} = \frac{9}{8}$$.

$$x = 9$$. The answer is $$\boxed{9}$$.

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