A simple pendulum of length 1 m is oscillating with an angular frequency 10 r a d s - 1 The support of the pendulum starts oscillating up and down with a small angular frequency of 1 r a d s - 1 and a

Question

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

TestHub · Accepted Answer

Angular frequency of simple pendulum, ω = g l As the support oscillates up and down, effective g changes ∆ g = 2 . ω 0 2 A = 2 × 1 2 × 10 - 2 m s - 2 = 0.02 m s - 2 Change in angular frequency d ω of the pendulum is given by d ω ω = - 1 2 ⋅ d g g ∆ ω ω = 1 2 ∆ g g = 1 2 × 0.02 10 = 0.001 r a d s - 1

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