Q. A particle of mass $m$ is executing oscillations about the origin on the $x$-axis with amplitude $A$. Its potential energy $U(x) = ax^{4}$ where $a$ is positive constant. The $x$-coordinate of mass where potential energy is one-third of the kinetic energy of particle is
A) $\frac{\pm A}{\sqrt{3}}$
B) $\frac{\pm A}{\sqrt{2}}$
C) $\frac{\pm A}{3}$
D) $\frac{\pm A}{2}$
Explanation
(b) Energy of oscillation, $E = \alpha A^{4}$
KE of mass at is
$K = E - U = \alpha(A^{4} - x^{4})$
$K = - 3U$
$\alpha\left( A^{4} - x^{4} \right) = 3\alpha x^{4}$
$x = \pm \frac{A}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.