A particle is performing simple harmonic moti | vedclass

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

Question

(C) For a particle performing simple harmonic motion,the speed $v$ at displacement $x$ is given by the formula:$v^2 = \omega^2(A^2 - x^2)$Expanding th

Vedclass · Accepted Answer

Vedclass · Answer

(C) For a particle performing simple harmonic motion,the speed $v$ at displacement $x$ is given by the formula:$v^2 = \omega^2(A^2 - x^2)$Expanding this equation,we get:$v^2 = \omega^2 A^2 - \omega^2 x^2$This equation is of the form $y = mx + c$,where $y = v^2$,$x = x^2$,$m = -\omega^2$ (slope),and $c = \omega^2 A^2$ (y-intercept).Since the slope is negative $(-\omega^2)$,the graph of $v^2$ versus $x^2$ is a straight line with a negative slope and a positive y-intercept.Therefore,the correct graph is a straight line starting from the y-axis and sloping downwards.

$A$ particle is performing simple harmonic motion with angular frequency $\omega$ and amplitude $A$. If $a$ is acceleration and $v$ is speed at any instant,then the graph showing the correct variation between $v^2$ and $x^2$ is (where $x$ is displacement):

Similar Questions

$A$ spring executes $S.H.M.$ with a mass of $1 \,kg$ attached to it. The force constant of the spring is $4 \,N/m$. If at any instant its velocity is $20 \,cm/s$, the displacement at that instant is (Amplitude of $S.H.M.$ is $0.4 \,m$)

What is the maximum velocity of a simple harmonic motion with an amplitude of $3 \ cm$ and a time period of $6 \ s$?

Maximum velocity and maximum acceleration of a particle executing $SHM$ are $\beta$ and $\alpha$ respectively. What will be its frequency?

$A$ body is executing $S.H.M.$ When its displacement from the mean position is $4 \, cm$ and $5 \, cm$,the corresponding velocity of the body is $10 \, cm/sec$ and $8 \, cm/sec$. Then the time period of the body is

For a simple harmonic motion with amplitude $A$ and time period $T$,what is the velocity at $x = \frac{A}{2}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module