First slide

Simple hormonic motion

Question

A particle of mass m is executing oscillations about the origin on the X-axis with amplitude A. Its potential energy is given as $U (x) = {βx}^{4}$ where $β$ is a positive constant. The x-coordinate of the particle, where the potential energy is one-third of the kinetic energy, is

Difficult

A

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

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

$\pm \frac{A}{3}$
D

$\pm \frac{A}{\sqrt{3}}$

Solution

$U = {βx}^{4} (Given)$
$∴ U_{\max} = β . A^{4}$
$k (x) = U_{\max} - U (x) = β . A^{4} - β X^{4} = β (A^{4} - x^{4})$
$U (x) = \frac{1}{3} K (k)$ (Given)
$∴ {βx}^{4} = \frac{1}{3} β (A^{4} - x^{4})$
$\Rightarrow 3 {βx}^{4} = {βA}^{4} - {βx}^{4}$
$4 {βx}^{4} = {βA}^{4} \Rightarrow x^{4} = \frac{A^{4}}{4}$
$\Rightarrow x = \pm \frac{A}{\sqrt{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App