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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 k₀, k₁, and a are all positive.

Correct answer: Acceleration = −k(x + a)

Solution

Simple harmonic motion (SHM) is characterized by acceleration being directly proportional to displacement and directed towards the mean position. The equation Acceleration = −k(x + a) satisfies this condition, as the negative sign indicates the restoring nature of the force.

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