A particle is executing S.H.M. of amplitude A | vedclass

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

Question

(D) The potential energy $(U)$ of a particle executing $S.H.M.$ at a displacement $x$ is given by $U = \frac{1}{2} k x^2$,where $k$ is the force const

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The potential energy $(U)$ of a particle executing $S.H.M.$ at a displacement $x$ is given by $U = \frac{1}{2} k x^2$,where $k$ is the force constant.The maximum potential energy $(U_{max})$ occurs at the extreme positions where $x = \pm A$,so $U_{max} = \frac{1}{2} k A^2$.According to the problem,the potential energy is half of its maximum value: $U = \frac{1}{2} U_{max}$.Substituting the expressions: $\frac{1}{2} k x^2 = \frac{1}{2} (\frac{1}{2} k A^2)$.Simplifying the equation: $x^2 = \frac{1}{2} A^2$.Taking the square root on both sides: $x = \pm \frac{A}{\sqrt{2}}$.Thus,the displacement is $\pm \frac{A}{\sqrt{2}}$.

$A$ particle is executing $S.H.M.$ of amplitude $A$. When the potential energy of the particle is half of its maximum value during the oscillation,its displacement from the equilibrium position is

Similar Questions

$A$ particle starts its oscillation from the equilibrium position with time period $T$. Find the ratio of kinetic energy to potential energy of the particle at time $t = \frac{T}{6}$.

The amplitude of a particle executing $SHM$ is $3\,cm$. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is: $.............cm$.

$A$ body starting at $t=0$ from the origin oscillates simple harmonically with a period of $4 \ s$. After what time will its kinetic energy be $75 \%$ of its total energy?

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

Assertion $(A)$: In $S.H.M$,kinetic and potential energy become equal when the distance is $1/\sqrt{2}$ times its amplitude. Reason $(R)$: The potential energy of a particle executing $S.H.M$ is periodic with time period being maximum at the extreme displacement.

Vedclass Test Series

Exam Paper Generator

Online Exam Module