Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles $\theta$₁,$\theta$₂ and $\theta$₃ respectively and released.The approximation sin $\theta$ = $\theta$ holds for all three angles,with $\theta$₃ $\theta$₂ $\theta$₁.How do the angular frequencies of the three pendulums compare? A) $ \omega $₃ $ \omega $₂ $ \omega $₁ B)Need to know amplitudes to answer this question. C)Need to know $\sqrt { g / L }$ to answer this question. D) $ \omega $₁ $ \omega $₂ $ \omega $₃ E) $ \omega $₁ = $ \omega $₂ = $ \omega $₃

Question

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles $\theta$₁,$\theta$₂ and $\theta$₃ respectively and released.The approximation sin $\theta$ = $\theta$ holds for all three angles,with $\theta$₃ > $\theta$₂ > $\theta$₁.How do the angular frequencies of the three pendulums compare? A) $ \omega $₃ > $ \omega $₂ > $ \omega $₁ B)Need to know amplitudes to answer this question. C)Need to know $\sqrt { g / L }$ to answer this question. D) $ \omega $₁ > $ \omega $₂ > $ \omega $₃ E) $ \omega $₁ = $ \omega $₂ = $ \omega $₃

Quizplus · Accepted Answer

The angular frequency of a simple pendulum depends only on the length of the string and the acceleration due to gravity, not on the amplitude, as long as the small angle approximation holds. Since all pendulums have the same length and the approximation is valid, their angular frequencies are equal.

Three Pendulums with Strings of the Same Length and Bobs θ\thetaθ

Three Pendulums with Strings of the Same Length and Bobs $\theta$