A simple pendulum of length 1 {~m} is oscillating with an angu

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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

1 rad / s

1 0^{- 5} rad / s

1 0^{- 3} rad / s

1 0^{- 1} rad / s

Views: 5,946 students

Updated on: Feb 4, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2019

Text solutionVerified

We know that time period of a pendulum is given by

T = 2 π \frac{l}{g}

So, angular frequency

ω = \frac{2 π}{T} = \frac{g}{I}

.....(i)
Now, differentiate both side w.r.t

g

∴ \frac{d ω}{d g} = \frac{1}{2 g I}

d ω = \frac{d g}{2 g 1}

.....(ii)
By dividing Eq. (ii) by Eq. (i), we get

\frac{d ω}{ω} = \frac{d g}{2 g}

]
Or we can write

\frac{Δ ω}{ω} = \frac{Δ g}{2 g}

.....(iii)
As

Δ g

is due to oscillation of support.

∴ Δ g = 2 ω^{2} A

(ω_{1} \to 1 rad / s

, support)
Putting value of

Δ g

in Eq. (iii) we get

\frac{Δ ω}{ω} = \frac{1}{2} \cdot \frac{2 ω _{1}^{2} A}{g} = \frac{ω _{1}^{2} A}{g} (A = 1 0^{- 2} m^{2})

\Rightarrow \frac{Δ ω}{ω} = \frac{1 \times 1 0 ^{- 2}}{10} = 1 0^{- 3} rad / s

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Alexander Discussed

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

15 mins ago

Discuss this question LIVE

15 mins ago

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Question Text	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
Updated On	Feb 4, 2023
Topic	Oscillations
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 10
Upvotes	997
Avg. Video Duration	7 min

Text solutionVerified

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