Answer
$\frac{1}{4}$ the total energy
Work Step by Step
$$E=\frac{1}{2}kA^2$$ $$U=\frac{1}{2}kx^2=\frac{1}{2}k(\frac{A}{2})^2=\frac{1}{8}kA^2$$ To find the fraction of the total energy that this potential energy is, create a ratio. $$\frac{\frac{1}{8}kA^2}{\frac{1}{2}kA^2}=\frac{1}{4}$$
