Q. A particle starts SHM from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3\frac{E}{4}$. Its displacement at that instant is
A) $\frac{a}{\sqrt{2}}$
B) $\frac{a}{2}$
C) $\frac{a}{\sqrt{\left( \frac{3}{2} \right)}}$
D) $\frac{a}{\sqrt{3}}$
Explanation
(b) $K = \frac{1}{2}\ m\omega^{2}(a^{2} - y^{2})$
$\frac{3}{4}\ E = \frac{1}{2}\ m\omega^{2}(a^{2} - y^{2})$
$\frac{3}{4}\ \left( \frac{1}{2}\ m\omega^{2}a^{2} \right) = \ \frac{1}{2}\ m\omega^{2}(a^{2} - y^{2})$
$y^{2} = a^{2} - \frac{3}{4}\ a^{2} = \frac{a^{2}}{4}$
$\Rightarrow$ $y = \frac{a}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.