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Question

What critical condition must the acceleration satisfy for a motion to be classified as simple harmonic?

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Explanation

**SHM representation** using sine or cosine equivalent with phase offset, ω relates to system parameters like mass and stiffness. Understanding ω and φ permits prediction of position at any time and comparison of two SHM via phase difference Δφ = φ₂ - φ₁. In SHM, acceleration must be proportional to displacement and directed opposite to it ( a = -ω² x ), ensuring harmonic oscillation about the mean position. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It is proportional to displacement and opposite in direction follows, reflecting SHM dependence

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