In SHM, the total energy $E$ is the sum of kinetic energy ($K$) and potential energy ($U$): $E=K+U=\frac{1}{2}m{v}^2+\frac{1}{2}k{x}^2$ For any displacement $x$: $E=\frac{1}{2}m{\omega }^2(A^2-x^2)+\frac{1}{2}k{x}^2=\frac{1}{2}k(A^2-x^2)+\frac{1}{2}k{x}^2$ $E=\frac{1}{2}k{A}^2$ This total energy remains constant throughout the cycle, oscillating between purely kinetic (at equilibrium, $x=0$) and purely potential (at extremes, $x=\pm A$).