(B) The acceleration of a particle in $\text{S.H.M.}$ is given by $a = -\omega^2 x$. Taking the magnitude, $|a| = \omega^2 |x|$.Given $x = 1 \ cm$ and

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The acceleration of a particle in $\text{S.H.M.}$ is given by $a = -\omega^2 x$. Taking the magnitude, $|a| = \omega^2 |x|$.Given $x = 1 \ cm$ and $a = 3 \ cm s^{-2}$, we have $3 = \omega^2 (1)$, which implies $\omega^2 = 3 \ s^{-2}$.The velocity of a particle in $\text{S.H.M.}$ is given by $v = \omega \sqrt{A^2 - x^2}$.Given $v = 6 \ cm s^{-1}$ at $x = 2 \ cm$, we substitute the values:$6 = \sqrt{3} \sqrt{A^2 - 2^2}$.Squaring both sides:$36 = 3 (A^2 - 4)$.Dividing by $3$:$12 = A^2 - 4$.$A^2 = 16$.$A = 4 \ cm$.

Class 11 Physics Oscillations Velocity of Simple Harmonic Motion

Difficult

$A$ particle is executing simple harmonic motion $\text{(S.H.M.).}$ Its acceleration at a distance of $1 \ cm$ from the mean position is $3 \ cm s^{-2}$. If its velocity is $6 \ cm s^{-1}$ when it is at a distance of $2 \ cm$ from its mean position, then the amplitude of $\text{S.H.M.}$ is,

TS EAMCET 2021 All TS EAMCET

A
$5 \ cm$
B
$4 \ cm$
C
$2 \sqrt{3} \ cm$
D
$3 \sqrt{2} \ cm$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Oscillations

Subtopic

Velocity of Simple Harmonic Motion

Previous Year

TS EAMCET 2021 Paper All TS EAMCET years →

Maximum speed of a particle in simple harmonic motion is $v_{max}.$ Then average speed of a particle in one complete oscillation is equal to

Medium

View Solution

The maximum velocity of a particle,executing $S$.$H$.$M$. with an amplitude $7 \ mm$ is $4.4 \ ms^{-1}$. The period of oscillation is $\left[\pi=\frac{22}{7}\right]$. (in $s$)

EasyMHT CET 2024

View Solution

$A$ particle executing simple harmonic motion has a maximum speed of $40 \,ms^{-1}$ and maximum acceleration of $60 \,ms^{-2}$. The period of oscillation is

MediumAP EAMCET 2021

View Solution

$A$ particle performs simple harmonic motion with a time period of $16 \ s$. At a time $t=2 \ s$, the particle passes through the origin and at $t=4 \ s$ its velocity is $4 \ m/s$. The amplitude of the motion is

EasyTS EAMCET 2022

View Solution

The velocity vector $v$ and displacement vector $x$ of a particle executing $SHM$ are related as $\frac{v dv}{dx} = -\omega^2 x$ with the initial condition $v = v_0$ at $x = 0$. The velocity $v$,when displacement is $x$,is

DifficultAIIMS 2015

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ particle is executing simple harmonic motion $\text{(S.H.M.).}$ Its acceleration at a distance of $1 \ cm$ from the mean position is $3 \ cm s^{-2}$. If its velocity is $6 \ cm s^{-1}$ when it is at a distance of $2 \ cm$ from its mean position, then the amplitude of $\text{S.H.M.}$ is,

Similar Questions

Maximum speed of a particle in simple harmonic motion is $v_{max}.$ Then average speed of a particle in one complete oscillation is equal to

The maximum velocity of a particle,executing $S$.$H$.$M$. with an amplitude $7 \ mm$ is $4.4 \ ms^{-1}$. The period of oscillation is $\left[\pi=\frac{22}{7}\right]$. (in $s$)

$A$ particle executing simple harmonic motion has a maximum speed of $40 \,ms^{-1}$ and maximum acceleration of $60 \,ms^{-2}$. The period of oscillation is

$A$ particle performs simple harmonic motion with a time period of $16 \ s$. At a time $t=2 \ s$, the particle passes through the origin and at $t=4 \ s$ its velocity is $4 \ m/s$. The amplitude of the motion is

The velocity vector $v$ and displacement vector $x$ of a particle executing $SHM$ are related as $\frac{v dv}{dx} = -\omega^2 x$ with the initial condition $v = v_0$ at $x = 0$. The velocity $v$,when displacement is $x$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module