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Question

A pendulum has \( L = 2.25 \, \text{m}, g = 9.8 \, \text{m/s}^2 \). What is its angular frequency?

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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. ω = √((g/L)) = √((9.8/2.25)) ≈ √(4.356) ≈ 2.087 rad/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 2.087 rad/s follows, reflecting SHM dependence on amplitude A, ω and system parameters.

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