energy in shm

Question

Total mechanical energy in SHM (amplitude A) is:

RankGuru · Accepted Answer

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

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Total mechanical energy of SHM (mass m, amplitude A)?