A small body of mass m is fixed to the middle of a stretched string of total length 2λ. In equilibrium the string tension is T₀. Find the angular frequency of small transverse oscillations. String mass is negligible and gravity is absent.
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Question

A small body of mass m is fixed to the middle of a stretched string of total length 2λ. In equilibrium the string tension is T₀. Find the angular frequency of small transverse oscillations. String mass is negligible and gravity is absent.

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G1 Physics · Accepted Answer

If the middle mass moves transversely by y, each half of the stretched string makes a small angle y/λ. The two transverse tension components give F≈−2T₀y/λ. Thus mÿ+(2T₀/λ)y=0 and ω=√(2T₀/mλ). Correct answer: A.