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Answer in brief · Q3

Q.On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
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From the derived frequency of a conical pendulum, n=12πgLcos⁡θn=\dfrac{1}{2\pi}\sqrt{\dfrac{g}{L\cos\theta}}, the frequency depends on three things: the LENGTH of the string L (a longer string gives a lower frequency), the SEMI-VERTICAL ANGLE θ\theta the string makes with the vertical (a larger θ\theta, i.e. a 'flatter' cone, means smaller cos⁡θ\cos\theta and hence a HIGHER frequency), and the local value of g (a larger g gives a higher frequency, e.g. the same pendulum would revolve faster on a planet with stronger surface gravity). Crucially, the mass m of the bob does NOT appear anywhere in this formula -- it cancelled out when dividing the two force equations T0sin⁡θ=mrω2T_0\sin\theta=mr\omega^2 and $ …

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