Answer
28.3 cm
Work Step by Step
Potential energy is equal to $\frac{1}{2}kx^2$. If $A$ is the amplitude, the total energy is $\frac{1}{2}kA^2$. If $\sqrt{2}A$ is the new amplitude, the new energy is $\frac{1}{2}(2)kA^2=kA^2$, double the original energy.
Therefore, the new amplitude must be $(20cm)(\sqrt{2})=28.3 cm$
