A mass m is suspended from a uniform spring and oscillates with frequency ν₁. The same spring is cut into two equal halves, and the same mass is suspended from one half. If the new frequency is ν₂, what is ν₂ /ν₁?
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Question

A mass m is suspended from a uniform spring and oscillates with frequency ν₁. The same spring is cut into two equal halves, and the same mass is suspended from one half. If the new frequency is ν₂, what is ν₂ /ν₁?

Options

G1 Physics · Accepted Answer

For a uniform spring, spring constant × length = constant. Therefore, kL = constant. If the spring length is reduced to half, L₂ = L₁ ÷ 2, then k₂ = 2k₁. The oscillation frequency is ν = (1 ÷ 2π)√(k ÷ m). Since the mass is unchanged, ν₂ ÷ ν₁ = √(k₂ ÷ k₁) = √2. Correct option: C.