Which one of the following equations of motion represents

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Which one of the following equations of motion represents simple harmonic motion?

1. Acceleration = – k(x + a)
2. Acceleration = k(x + a)
3. Acceleration = kx
4. Acceleration = – k₀x + k₁x² where k, k₀, k₁ and a are all postive.

Correct Option: A

a = – kX, X = x + a.
In simple harmonic motion acceleration is directly proportional to the displacement from the mean position. Also the acceleration is in the opposite direction of displacement.