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Damped and forced oscillations

The amplitude of a damped oscillator decreases to 0.9 times it

Question

Medium

Solving time: 3 mins

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 s$ . In another $10 s$ , it will decrease to $α$ times its original magnitude, where $α$ equals

0.7

0.81

0.729

0.6

Views: 6,262 students

Updated on: Oct 3, 2023

Book:

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

Exam:

JEE Mains 2013

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Benjamin Discussed

The amplitude of a damped oscillator decreases to

0.9

times its original magnitude in

5 s

. In another

10 s

, it will decrease to

α

times its original magnitude, where

α

equals

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Amplitude of damped oscillator is given by

A = A_{0} e^{- \frac{b t}{2 m}}

After

5 s, 0.9 A_{0} = A_{0} e^{- \frac{b ( 5 )}{2 m}}

\Rightarrow 0.9 = e^{- \frac{b ( 5 )}{2 m}}

After,

10 s, A = A_{0} e^{- b \frac{( 15 )}{2 m}}

\Rightarrow A = A_{0} (e^{- \frac{5 b}{2 m})^{3}}

A = 0.729 A_{0}

Hence,

α = 0.729

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Question Text	The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 s$ . In another $10 s$ , it will decrease to $α$ times its original magnitude, where $α$ equals
Updated On	Oct 3, 2023
Topic	Oscillations
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	583
Avg. Video Duration	10 min

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 s$ . In another $10 s$ , it will decrease to $α$ times its original magnitude, where $α$ equals

Text solutionVerified

Filo tutor solutions (5)

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The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s. In another 10 s, it will decrease to α times its original magnitude, where α equals

Text solutionVerified

Filo tutor solutions (5)

Questions from JEE Mains 2013 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

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The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 s$ . In another $10 s$ , it will decrease to $α$ times its original magnitude, where $α$ equals