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

Engineering

Physics

SHM of Simple Pendulum

Question

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

10^–1 rad/s

1 rad/s

10^–5 rad/s

10^–3 rad/s

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Angular frequency of pendulum

$ω \propto \sqrt{\frac{g_{eff}}{ℓ}}$

$∴ \frac{Δω}{ω} = \frac{1}{2} \frac{{Δg}_{eff}}{g_{eff}}$

$Δω = \frac{1}{2} \frac{Δg}{g} \times ω$

$= \frac{1}{2} \times \frac{2 ({Aω}_{5}^{s})}{10}$

$\Rightarrow \frac{Δω}{ω} = \frac{1 \times 10^{- 2}}{10} = 10^{- 3}$