## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

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 $(20cm)(\sqrt{2})=28.3 cm$