Using the second Law of Newton, F = m * a, you know that acceleration is maximum when the force is maximum.
Using Hooke's Law, F = K Δx, you know that the force is maximum when the displacement from the equilibrium (Δx) is maximum.
So the answer is that the acceleration is maximum at the maximum amplitude x = a.
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Well according to Newton’s first law of motion, a body will remain in the state of rest or linear motion provided that an *external force* has been applied. So no, a force doesn’t need to keep a body to remain in linear motion, because F=ma, during uniform linear motion velocity is constant, hence acceleration is zero, so F=0
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