A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad / s . The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad / s and an ampl

Question

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad / s . The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad / s and an amplitude of 1 0 − 2 m . The relative change in the angular frequency of the pendulum is best given by :

TestHub · Accepted Answer

Angular frequency of pendulum ω = ℓ g ​ ​ ∴ relative change in angular frequency ω Δ ω ​ = 2 1 ​ g Δ g ​ [ as length remains constant ] Δ g = 2 A ω s 2 ​ [ ω s ​ = angular frequency of support and, A = amplitude] ω Δ ω ​ = 2 1 ​ × g 2 A ω S 2 ​ ​ Δ ω = 2 1 ​ × 10 2 × 1 2 × 1 0 − 2 ​ = 1 0 − 3 rad / sec

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