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Problem 7 - Entrance Test

Two identical pendulums are coupled with a weak spring. The system undergoes normal mode oscillations with frequencies f₁ and f₂. If their individual frequencies are f₀, what is the relation between f₁ and f₂?

Correct: A

In coupled pendulums, the normal mode frequencies satisfy f₁² + f₂² = 2f₀². When coupling is weak, f₁ ≈ f₀ - Δ and f₂ ≈ f₀ + Δ, leading to f₁f₂ ≈ f₀².