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Then, we have the recursion \begin{equation}  E_i=\frac{1}{\tau}{\sqrt{\frac{m\pi^2 E_i=\frac{1}{\tau}\sqrt{\frac{m\pi^2  x_0^2}{2}}\sqrt{E} \end{equation}  Which does converge on the correct energy if $\tau=\pi/\omega$.  ______REVISE________ %______REVISE________  Solving for $x(t)$ gives $exp(i\omega t)$, which has real part $cos(\omega t)$. Therefore substituting and rearranging and integrating gives \begin{equation}