The total mechanical energy of a particle of mass $m$ in SHM with amplitude $A$ and angular frequency $\omega$ is:

Total energy is conserved during SHM and equals the maximum kinetic energy (at the mean position) or the maximum potential energy (at the extreme): $E = \dfrac{1}{2} m v_{\max}^2 = \dfrac{1}{2} m (A\omega)^2 = \dfrac{1}{2} m \omega^2 A^2$. Equivalently, $E = \dfrac{1}{2} k A^2$ for a spring-mass system, using $\omega^2 = k/m$. Quadratic in amplitude: doubling the amplitude *quadruples* the total energy. Same scaling as kinetic energy with velocity.