EQUATION

Pendulum Angular Frequency

Gives the angular frequency ω = √(g/L) of a small-angle pendulum

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The equation

EQ.PENDULUM-FREQUENCY
\omega = \sqrt{\frac{g}{L}}
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What it solves

Gives the angular frequency ω = √(g/L) of a small-angle pendulum. Knowing ω, you can write x(t) = A·cos(ωt + φ) for the angle as a function of time.

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When to use it

Whenever the problem asks for frequency or angular frequency rather than period. Directly sets the oscillation rate for a coupled-pendulum analysis.

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When NOT to use it

Same restrictions as the small-angle period: amplitudes must be small (θ₀ ≲ 15°). Does not account for air resistance or pivot friction.

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Common mistakes

Swapping the formula to ω = √(L/g) — it is g over L, not L over g. Confusing ω (rad/s) with f (Hz); they are related by ω = 2πf. Using the bob mass in the formula — ω is independent of mass.

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Topics that use this equation

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Problems using this equation