Question

In SHM, kinetic energy is $(1 / 4)^{\text {th }}$ of the total energy at a displacement equal to
(Here $A$ is the amplitude of oscillations.)

• A. $\frac{A}{2}$
• B. $\frac{A}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{2} A$
• D. $\frac{2}{\sqrt{3}} A$

Answer 1

Answer: (C)

In SHM, Kinetic energy, $K=\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)$
Total energy, $E=\frac{1}{2} m \omega^{2} A^{2}$.
As $K=\frac{E}{4}$
$\therefore \frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)=\frac{1}{4}\left(\frac{1}{2} m \omega^{2} A^{2}\right)$
or $4 A^{2}-4 x^{2}=A^{2}$ or $4 x^{2}=3 A^{2}$
or $x=\frac{\sqrt{3}}{2} A$