Practice question
Question
A pendulum has \( L = 0.5 \, \text{m}, g = 9.8 \, \text{m/s}^2 \). What is its angular frequency?
Explanation
**Real oscillators** experience damping, amplitude decreasing with time. Critical damping returns to equilibrium fastest without oscillation, overdamping slows return, underdamping shows decaying oscillations, classification based on b relative to 2mω₀, important for practical systems. ω = √((g/L)) = √((9.8/0.5)) = √(19.6) ≈ 4.43 rad/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 4.43 rad/s follows, reflecting SHM dependence on amplitude A, ω and system parameters.
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