Conditions for simple harmonic motion

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Oscillation in which the **acceleration is proportional to the displacement** from equilibrium and is always directed **back toward equilibrium**.

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$a = -\omega^{2}x$ — **given** in the data booklet. a = acceleration, ω = angular frequency, x = displacement.

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The acceleration points **opposite to the displacement** — always back toward equilibrium (the restoring direction).

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A force that always acts to push or pull the object **back toward its equilibrium (resting) position**.

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The central resting position where the object would sit still — where the displacement x = 0.

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1. Acceleration **proportional to** displacement. 2. Acceleration directed **back toward equilibrium** (opposite to x).

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A **straight line through the origin** with a **negative slope** equal to −ω².

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There is a **restoring force** (and acceleration) directed **back to equilibrium** that is **proportional to the displacement** — exactly the condition a = −ω²x.

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The steady loss of energy from an oscillation (to friction or drag), so each successive swing has a **smaller amplitude**.

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The **amplitude slowly decreases** over many cycles while the **period stays almost the same**.

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Yes — same form as a = −ω²x, so ω² = 25 → **ω = 5.0 rad s⁻¹**.