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Q.

A simple pendulum of length 1 m  is oscillating with an angular frequency 10 rad/s. If the support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s with an amplitude of 102 m. Find the relative change in the angular frequency of the pendulum.

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a

101 rad/s

b

103 rad/s

c

1 rad/s

d

105 rad/s

answer is B.

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Detailed Solution

Angular Frequency ω=g

Δωω=12Δgg

Δg is due to oscillation of support. 

Δg=2ω12A1 Where ω1 is the angular frequency of oscillation of support A,

 Δωω=122ω12A1g (A1 is the amplitude of oscillation.)

 =12×2×12×10210=103

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