A particle executes SHM of amplitude A. The d | vedclass

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

Question

(C) The kinetic energy $(KE)$ of a particle in $SHM$ at a distance $x$ from the mean position is given by $KE = \frac{1}{2} m \omega^2 (A^2 - x^2)$.Th

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}} A$

Vedclass · Answer

(C) The kinetic energy $(KE)$ of a particle in $SHM$ at a distance $x$ from the mean position is given by $KE = \frac{1}{2} m \omega^2 (A^2 - x^2)$.The potential energy $(PE)$ of the particle at the same position is given by $PE = \frac{1}{2} m \omega^2 x^2$.According to the problem,$KE = PE$:$\frac{1}{2} m \omega^2 (A^2 - x^2) = \frac{1}{2} m \omega^2 x^2$.Canceling the common terms $\frac{1}{2} m \omega^2$ from both sides,we get:$A^2 - x^2 = x^2$.Rearranging the terms,we get $A^2 = 2x^2$.Solving for $x$,we find $x^2 = \frac{A^2}{2}$,which implies $x = \pm \frac{A}{\sqrt{2}}$.

$A$ particle executes $SHM$ of amplitude $A$. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:

Similar Questions

If a particle is executing simple harmonic motion with time period $T$,then the time period of its total mechanical energy is ...........

The average energy possessed by an oscillator at a temperature $300 \ K$ is (Boltzmann constant $= 1.38 \times 10^{-23} \ J K^{-1}$).

$A$ block is executing $SHM.$ Let the time period of variation of velocity be $T_1$ and time period of variation of kinetic energy be $T_2.$ The relation between $T_1$ and $T_2$ is

$A$ particle starts oscillating simple harmonically from its equilibrium position with time period $T$. What is the ratio of potential energy to kinetic energy of the particle at time $t = \frac{T}{12}$? (Given: $\sin(\frac{\pi}{6}) = \frac{1}{2}$)

For a particle $P$ performing $S.H.M.$, when displacement is $x$, potential energy and restoring force acting on it are denoted by $E$ and $F$ respectively. The relation between $x, E$, and $F$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module