Is the acceleration of a simple harmonic oscillator ever zero if so where?

Answer:

Yes; the acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always act TOWARDS the equilibrium position (because it's a restorative force), then the force and acceleration must change their sign as the mass crosses the e.p., and therefore must be zero instantaneously at the e.p.

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