Assertion : In simple harmonic motion,the mot | vedclass

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

Question

(A) Simple Harmonic Motion $(SHM)$ is defined as a periodic motion in which the restoring force is directly proportional to the displacement and acts

Vedclass · Accepted Answer

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

Vedclass · Answer

(A) Simple Harmonic Motion $(SHM)$ is defined as a periodic motion in which the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. This results in to-and-fro motion about a mean position. The velocity of a particle in $SHM$ is given by the formula $v = \omega \sqrt{A^2 - x^2}$,where $A$ is the amplitude,$x$ is the displacement,and $\omega$ is the angular frequency. The original reason provided used $k$ instead of $A$,which is notationally incorrect for amplitude. However,the formula correctly describes the velocity variation in $SHM$,which confirms the periodic and to-and-fro nature of the motion. Thus,both statements are correct,and the velocity expression explains the nature of the motion.

$Assertion :$ In simple harmonic motion,the motion is to and fro and periodic.
$Reason :$ Velocity of the particle $(v) = \omega \sqrt {A^2 - x^2}$ (where $x$ is the displacement and $A$ is the amplitude).

Similar Questions

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \text{ m}$ represents the motion of a particle executing simple harmonic motion,the amplitude and time period of motion,respectively,are

Draw plots for initial phase $\phi = 0$ for different periods.

Define periodic time.

$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:

$A$ simple harmonic motion is represented by $y = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t) \ cm$. The amplitude and time period of the motion are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$Assertion :$ In simple harmonic motion,the motion is to and fro and periodic. $Reason :$ Velocity of the particle $(v) = \omega \sqrt {A^2 - x^2}$ (where $x$ is the displacement and $A$ is the amplitude).