Total mechanical energy in SHM is $E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2A^2$, constant throughout the motion. At any position $x$: $KE = \frac{1}{2}k(A^2 - x^2)$ and $PE = \frac{1}{2}kx^2$. Important ratios: at $x = A/\sqrt{2}$, $KE = PE = E/2$; at $x = A/2$, $KE = 3E/4$ and $PE = E/4$. Both KE and PE oscillate with frequency $2\omega$ (twice the oscillation frequency). The time-averaged values are $\langle KE \rangle = \langle PE \rangle = E/2$. Energy is proportional to $A^2$: doubling the amplitude quadruples the energy.