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

Options

(a) Acceleration = -k(x + a)
(b) Acceleration = k(x + a)
(c) Acceleration = kx
(d) Acceleration = -k₀x+ k₁x² where k, k₀, k₁ and a are +ve

Correct Answer:

Acceleration = -k(x + a)

Explanation:

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.