A particle is performing simple harmonic moti | vedclass

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

Question

(B) For a particle in simple harmonic motion $(SHM)$:$(i)$ The velocity $v$ as a function of displacement $x$ is given by $v = \omega \sqrt{A^2 - x^2}

Vedclass · Accepted Answer

$(ii)$ and $(iii)$

Vedclass · Answer

(B) For a particle in simple harmonic motion $(SHM)$:$(i)$ The velocity $v$ as a function of displacement $x$ is given by $v = \omega \sqrt{A^2 - x^2}$. Squaring both sides,$v^2 = \omega^2(A^2 - x^2)$,which represents an ellipse,not a parabola. Thus,$(i)$ is incorrect.$(ii)$ The velocity as a function of time is $v(t) = A\omega \cos(\omega t)$,which is a sinusoidal function. Thus,$(ii)$ is correct.$(iii)$ The acceleration is $a(t) = -A\omega^2 \sin(\omega t)$. From $v = A\omega \cos(\omega t)$ and $a = -A\omega^2 \sin(\omega t)$,we have $(v/A\omega)^2 + (a/A\omega^2)^2 = \cos^2(\omega t) + \sin^2(\omega t) = 1$. This is the equation of an ellipse. Thus,$(iii)$ is correct.Therefore,statements $(ii)$ and $(iii)$ are correct.

$A$ particle is performing simple harmonic motion. Which of the following statements are correct?
$(i)$ Its velocity-displacement graph is parabolic in nature.
$(ii)$ Its velocity-time graph is sinusoidal in nature.
$(iii)$ Its velocity-acceleration graph is elliptical in nature.

Similar Questions

The velocity of a particle in simple harmonic motion at displacement $y$ from the mean position is

$A$ particle is in simple harmonic motion. The equation of its motion is $x = 5 \sin \left( 4t - \frac{\pi}{6} \right)$,where $x$ is its displacement. If the displacement of the particle is $3$ units,then its velocity is:

If the maximum velocity and maximum acceleration of a particle executing simple harmonic motion are respectively $5 \,m \,s^{-1}$ and $10 \,m \,s^{-2}$, then the time period of oscillation of the particle is

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{-2} \cos(\pi t) \text{ m}$. The time at which the maximum speed first occurs is (in $\text{ s}$)

The graph between velocity and displacement of a particle executing $S.H.M.$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$A$ particle is performing simple harmonic motion. Which of the following statements are correct?$(i)$ Its velocity-displacement graph is parabolic in nature.$(ii)$ Its velocity-time graph is sinusoidal in nature.$(iii)$ Its velocity-acceleration graph is elliptical in nature.