Energy of Simple Harmonic Oscillator

Question

At what position is the kinetic energy of a simple harmonic mass-spring system double its potential energy, as a fraction of the amplitude?

Answer 1

Total energy:

kA²/2 = mv²/2 + kx²/2

mv²/2 = 2(kx²/2) = kx² ⇒

kA²/2 = kx² + kx²/2 = (3/2)kx²

A² = 3x²

x = A/√3