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A particle performs simple harmonic motion with amplitude A. I

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A particle performs simple harmonic motion with amplitude $A$ . Its speed is trebled at the instant that it is at a distance $\frac{2}{3} A$ from equilibrium position. The new amplitude of the motion is

\frac{A}{3} 41

3 A

A 3

\frac{7}{3} A

Views: 5,542 students

Updated on: Jan 1, 2023

Book:

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

Exam:

JEE Mains 2016

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A particle performs simple harmonic motion with amplitude

A

. Its speed is trebled at the instant that it is at a distance

\frac{2}{3} A

from equilibrium position. The new amplitude of the motion is

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

The velocity of a particle executing SHM at any instant is defined as the time rate of change of its displacement at that instant.

v = ω A^{2} - x^{2}

where,

ω

is the angular frequency,

A

is amplitude and

x

is the displacement of a particle.
Suppose that the new amplitude of the motion be

A^{'}

.
Initial velocity of a particle performs SHM,

v^{2} = ω^{2} [A^{2} - (\frac{2 A}{3})^{2}]

where

A

is initial amplitude and

ω

is the angular frequency.
Final velocity,

(3 v)^{2} = ω^{2} [A^{'2} - (\frac{2 A}{3})^{2}]

From Eqs. (i) and (ii), we get

\frac{1}{9} = \frac{A ^{2} - \frac{4 A ^{2}}{9}}{A ^{'2} - \frac{4 A ^{2}}{9}} \Rightarrow A^{'} = \frac{7 A}{3}

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Question Text	A particle performs simple harmonic motion with amplitude $A$ . Its speed is trebled at the instant that it is at a distance $\frac{2}{3} A$ from equilibrium position. The new amplitude of the motion is
Updated On	Jan 1, 2023
Topic	Oscillations
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 7
Upvotes	866
Avg. Video Duration	6 min

A particle performs simple harmonic motion with amplitude $A$ . Its speed is trebled at the instant that it is at a distance $\frac{2}{3} A$ from equilibrium position. The new amplitude of the motion is

Text solutionVerified

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A particle performs simple harmonic motion with amplitude $A$ . Its speed is trebled at the instant that it is at a distance $\frac{2}{3} A$ from equilibrium position. The new amplitude of the motion is